

A271980


Numbers k such that 3*k^2 + 39*k + 37 is prime.


34



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 44, 45, 46, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 68, 69, 70, 71, 72, 79, 84, 86, 88, 89, 90, 91, 92
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OFFSET

1,3


COMMENTS

From Peter Bala, Apr 16 2018: (Start)
Let P(n) = 3*n^2 + 39*n + 37. The absolute values of the polynomial P(2*n  29) = 12*n^2  270*n + 1429 for n from 0 to 27 are distinct primes, except at n = 14 when the value is 1.
The absolute values of the polynomial 3*P((n  20)/3) = n^2  n  269 for n from 0 to 42 are either prime or 3 times a prime.
The absolute values of the polynomial 3*P((4*n  89)/3) = 16*n^2  556*n + 4561 for n from 0 to 27 are either prime or 3 times a prime. (End)


LINKS

Robert Price, Table of n, a(n) for n = 1..3510
Eric Weisstein's World of Mathematics, PrimeGenerating Polynomials


EXAMPLE

4 is in this sequence since 3*4^2 + 39*4 + 37 = 48+156+37 = 241 is prime.


MATHEMATICA

Select[Range[0, 100], PrimeQ[3*#^2 + 39*# + 37] &]


PROG

(PARI) isok(n) = isprime(3*n^2 + 39*n + 37); \\ Michel Marcus, Apr 17 2016
(PARI) lista(nn) = for(n=0, nn, if(ispseudoprime(3*n^2+39*n+37), print1(n, ", "))); \\ Altug Alkan, Apr 18 2016
(Magma) [n: n in [0..100] IsPrime(3*n^2+39*n+37)]; // Vincenzo Librandi, Apr 19 2018


CROSSREFS

Cf. A256585, A050265  A050268, A005846, A007641, A007635, A048988.
Sequence in context: A342523 A249830 A300473 * A353886 A191882 A098451
Adjacent sequences: A271977 A271978 A271979 * A271981 A271982 A271983


KEYWORD

nonn,easy,less


AUTHOR

Robert Price, Apr 17 2016


STATUS

approved



