A271980 Numbers k such that 3*k^2 + 39*k + 37 is prime.

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

Offset: 1

Author

Robert Price, Apr 17 2016

Keywords

• nonn
• easy
• less

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)

Examples

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

Links

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

Crossrefs

Cf. A256585, A050265 - A050268, A005846, A007641, A007635, A048988.

Programs

Magma

[n: n in [0..100] |IsPrime(3*n^2+39*n+37)]; // Vincenzo Librandi, Apr 19 2018

Mathematica

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

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