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 A007641 Primes of the form 2*n^2 + 29. (Formerly M5219) 49
 29, 31, 37, 47, 61, 79, 101, 127, 157, 191, 229, 271, 317, 367, 421, 479, 541, 607, 677, 751, 829, 911, 997, 1087, 1181, 1279, 1381, 1487, 1597, 1951, 2207, 2341, 2621, 2767, 2917, 3229, 3391, 3557, 3727, 4079, 4261, 4447, 4637, 4831, 5231, 5437 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The first 29 terms of 2*n^2 + 29 (n = 0 to 28) are primes. This was discovered by Adrien-Marie Legendre. The sequence and its first 8 terms appear in the novel Code to Zero by Ken Follett. - Amiram Eldar, Apr 08 2017 Let P(n) = 2*n^2 + 29. The polynomial P(2*n - 28) = 8*n^2 - 224*n + 1597 produces prime values (not distinct) for n = 0 to 28. The polynomial P(3*n - 55) = 18*n^2 - 660*n + 6079 produces distinct prime values for n = 0 to 27. Cf. A050265. - Peter Bala, Apr 16 2018 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). Ken Follett, Code to Zero, New York: Signet, 2001, p. 18. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Adrien-Marie Legendre, Essai sur la thÃ©orie des nombres, Paris: Duprat, 1798, p. 10. Eric Weisstein's World of Mathematics, Prime-generating Polynomial. MATHEMATICA Select[Table[2 n^2 + 29, {n, 0, 70}], PrimeQ] (* Vincenzo Librandi, Mar 20 2013 *) PROG (MAGMA) [a: n in [0..60] | IsPrime(a) where a is 2*n^2+29]; // Vincenzo Librandi, Mar 20 2013 CROSSREFS Cf. A005846, A050265. Sequence in context: A031062 A054056 A108112 * A050656 A050667 A288879 Adjacent sequences:  A007638 A007639 A007640 * A007642 A007643 A007644 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by Erich Friedman, Feb 09 2002 STATUS approved

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Last modified December 10 23:29 EST 2019. Contains 329910 sequences. (Running on oeis4.)