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A007641
Primes of the form 2*k^2 + 29.
(Formerly M5219)
55
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
OFFSET
1,1
COMMENTS
The first 29 terms of 2*k^2 + 29 (k = 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(k) = 2*k^2 + 29. The polynomial P(2*k - 28) = 8*k^2 - 224*k + 1597 produces prime values (not distinct) for k = 0 to 28. The polynomial P(3*k - 55) = 18*k^2 - 660*k + 6079 produces distinct prime values for k = 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
Adrien-Marie Legendre, Essai sur la théorie 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
(PARI) list(lim)=my(v=List(), t); for(n=0, sqrtint((lim-29)\2), if(isprime(t=2*n^2+29), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Jan 20 2022
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
Edited by Erich Friedman, Feb 09 2002
STATUS
approved