Perrin number (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Perrin number" in English language version.

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archive.org

Perrin (1899) Perrin, R. [in French] (1899). "Question 1484". L'Intermédiaire des Mathématiciens. 6. Gauthier-Villars et fils: 76–77.
Perrin (1899) translated from the French Perrin, R. [in French] (1899). "Question 1484". L'Intermédiaire des Mathématiciens. 6. Gauthier-Villars et fils: 76–77.

arxiv.org

Grantham (2010), Stephan (2020) Grantham, Jon (2010). "There are infinitely many Perrin pseudoprimes". Journal of Number Theory. 130 (5): 1117–1128. arXiv:1903.06825. doi:10.1016/j.jnt.2009.11.008. Stephan, Holger (2020). "Millions of Perrin pseudoprimes including a few giants". arXiv:2002.03756v1 [math.NA].

doi.org

Lucas (1878) Lucas, E. (1878). "Théorie des fonctions numériques simplement périodiques". American Journal of Mathematics (in French). 1 (3). Johns Hopkins University Press: 229–231. doi:10.2307/2369311. JSTOR 2369311.
Adams & Shanks (1982) Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.
Kurtz, Shanks & Williams (1986) Kurtz, G. C.; Shanks, Daniel; Williams, H. C. (1986). "Fast primality tests for numbers less than 50∙10⁹". Mathematics of Computation. 46 (174). American Mathematical Society: 691–701. doi:10.1090/S0025-5718-1986-0829639-7. JSTOR 2008007.
Füredi (1987) Füredi, Zoltán (1987). "The number of maximal independent sets in connected graphs". Journal of Graph Theory. 11 (4): 463–470. doi:10.1002/jgt.3190110403.
Adams & Shanks (1982, p. 255) Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.
Grantham (2010), Stephan (2020) Grantham, Jon (2010). "There are infinitely many Perrin pseudoprimes". Journal of Number Theory. 130 (5): 1117–1128. arXiv:1903.06825. doi:10.1016/j.jnt.2009.11.008. Stephan, Holger (2020). "Millions of Perrin pseudoprimes including a few giants". arXiv:2002.03756v1 [math.NA].
Adams & Shanks (1982, p. 265, 269-270) Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.
Adams & Shanks (1982, p. 275), Kurtz, Shanks & Williams (1986, p. 694). This was later confirmed for $n < 10 14$ by Steven Arno (1991). Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637. Kurtz, G. C.; Shanks, Daniel; Williams, H. C. (1986). "Fast primality tests for numbers less than 50∙10⁹". Mathematics of Computation. 46 (174). American Mathematical Society: 691–701. doi:10.1090/S0025-5718-1986-0829639-7. JSTOR 2008007. Arno, Steven (1991). "A note on Perrin pseudoprimes". Mathematics of Computation. 56 (193). American Mathematical Society: 371–376. Bibcode:1991MaCom..56..371A. doi:10.1090/S0025-5718-1991-1052083-9. JSTOR 2008548.
The signature does give discriminating information on the remaining two types of primes. For example, the smallest Q-type pseudoprime 50,972,694,899,204,437,633 computed by Holger Stephan (2019) is exposed by signature conditions 14a and 14c in Adams & Shanks (1982, p. 257). Stephan, Holger (2019). Perrin pseudoprimes (WIAS Research Data No. 4). Berlin: Weierstrass Institute. doi:10.20347/WIAS.DATA.4. Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.
Kurtz, Shanks & Williams (1986, p. 697) Kurtz, G. C.; Shanks, Daniel; Williams, H. C. (1986). "Fast primality tests for numbers less than 50∙10⁹". Mathematics of Computation. 46 (174). American Mathematical Society: 691–701. doi:10.1090/S0025-5718-1986-0829639-7. JSTOR 2008007.
Stephan (2019) Stephan, Holger (2019). Perrin pseudoprimes (WIAS Research Data No. 4). Berlin: Weierstrass Institute. doi:10.20347/WIAS.DATA.4.
Adams & Shanks (1982, p. 280-283) Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.
Stephan (2019) Stephan, Holger (2019). Perrin pseudoprimes (WIAS Research Data No. 4). Berlin: Weierstrass Institute. doi:10.20347/WIAS.DATA.4.

harvard.edu

ui.adsabs.harvard.edu

Adams & Shanks (1982, p. 275), Kurtz, Shanks & Williams (1986, p. 694). This was later confirmed for $n < 10 14$ by Steven Arno (1991). Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637. Kurtz, G. C.; Shanks, Daniel; Williams, H. C. (1986). "Fast primality tests for numbers less than 50∙10⁹". Mathematics of Computation. 46 (174). American Mathematical Society: 691–701. doi:10.1090/S0025-5718-1986-0829639-7. JSTOR 2008007. Arno, Steven (1991). "A note on Perrin pseudoprimes". Mathematics of Computation. 56 (193). American Mathematical Society: 371–376. Bibcode:1991MaCom..56..371A. doi:10.1090/S0025-5718-1991-1052083-9. JSTOR 2008548.

jstor.org

Lucas (1878) Lucas, E. (1878). "Théorie des fonctions numériques simplement périodiques". American Journal of Mathematics (in French). 1 (3). Johns Hopkins University Press: 229–231. doi:10.2307/2369311. JSTOR 2369311.
Adams & Shanks (1982) Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.
Kurtz, Shanks & Williams (1986) Kurtz, G. C.; Shanks, Daniel; Williams, H. C. (1986). "Fast primality tests for numbers less than 50∙10⁹". Mathematics of Computation. 46 (174). American Mathematical Society: 691–701. doi:10.1090/S0025-5718-1986-0829639-7. JSTOR 2008007.
Adams & Shanks (1982, p. 255) Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.
Adams & Shanks (1982, p. 265, 269-270) Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.
Adams & Shanks (1982, p. 275), Kurtz, Shanks & Williams (1986, p. 694). This was later confirmed for $n < 10 14$ by Steven Arno (1991). Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637. Kurtz, G. C.; Shanks, Daniel; Williams, H. C. (1986). "Fast primality tests for numbers less than 50∙10⁹". Mathematics of Computation. 46 (174). American Mathematical Society: 691–701. doi:10.1090/S0025-5718-1986-0829639-7. JSTOR 2008007. Arno, Steven (1991). "A note on Perrin pseudoprimes". Mathematics of Computation. 56 (193). American Mathematical Society: 371–376. Bibcode:1991MaCom..56..371A. doi:10.1090/S0025-5718-1991-1052083-9. JSTOR 2008548.
The signature does give discriminating information on the remaining two types of primes. For example, the smallest Q-type pseudoprime 50,972,694,899,204,437,633 computed by Holger Stephan (2019) is exposed by signature conditions 14a and 14c in Adams & Shanks (1982, p. 257). Stephan, Holger (2019). Perrin pseudoprimes (WIAS Research Data No. 4). Berlin: Weierstrass Institute. doi:10.20347/WIAS.DATA.4. Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.
Kurtz, Shanks & Williams (1986, p. 697) Kurtz, G. C.; Shanks, Daniel; Williams, H. C. (1986). "Fast primality tests for numbers less than 50∙10⁹". Mathematics of Computation. 46 (174). American Mathematical Society: 691–701. doi:10.1090/S0025-5718-1986-0829639-7. JSTOR 2008007.
Adams & Shanks (1982, p. 280-283) Adams, William; Shanks, Daniel (1982). "Strong primality tests that are not sufficient". Mathematics of Computation. 39 (159). American Mathematical Society: 255–300. doi:10.1090/S0025-5718-1982-0658231-9. JSTOR 2007637.

ntheory.org

None of the 2402549 Lucas-Selfridge pseudoprimes below 10¹⁵ listed by Dana Jacobsen (2020) is also a Perrin pseudoprime. Jacobsen, Dana (2020). "Pseudoprime statistics and tables". ntheory.org. Retrieved 7 March 2024. #LPSP Lucas-Selfridge

oeis.org

Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence (or Ondrej Such sequence): a(n) = a(n-2) + a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A078712 (Series expansion of (-3 - 2*x)/(1 + x - x^3) in powers of x)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A112881 (Indices of prime Perrin numbers; values of n such that A001608(n) is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A074788 (Prime numbers in the Perrin sequence b(n+1) = b(n-1) + b(n-2) with initial values b(1)=3, b(2)=0, b(3)=2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A000918 (a(n) = 2^n - 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Malo (1900), Jarden (1966) Malo, E. (1900). "Réponse à 1484". L'Intermédiaire des Mathématiciens. 7. Gauthier-Villars et fils: 280–282, 312–314. Jarden, Dov (1966). Recurring sequences (PDF) (2 ed.). Jerusalem: Riveon LeMatematika. pp. 86–93.
Sloane, N. J. A. (ed.). "Sequence A013998 (Unrestricted Perrin pseudoprimes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A018187 (Restricted Perrin pseudoprimes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A275612 (Restricted Perrin pseudoprimes (Adams and Shanks definition))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A275613 (Restricted Perrin pseudoprimes (Grantham definition).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

wikipedia.org

fr.wikipedia.org

Perrin (1899) Perrin, R. [in French] (1899). "Question 1484". L'Intermédiaire des Mathématiciens. 6. Gauthier-Villars et fils: 76–77.
Perrin (1899) translated from the French Perrin, R. [in French] (1899). "Question 1484". L'Intermédiaire des Mathématiciens. 6. Gauthier-Villars et fils: 76–77.