A253239 Numbers k such that k^2 + k + 72491 is prime.

1, 2, 3, 6, 7, 11, 12, 13, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 53, 55, 56, 57, 58, 59, 64, 65, 66, 67, 72, 73, 74, 75, 77, 78, 81, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 98, 100

Offset: 1

Author

Eric Chen, Apr 19 2015

Keywords

• nonn
• easy

Comments

Of the first 10000 natural numbers, 4534 are in this sequence, making the density about 45%, quite large! (However, 72491 is not prime; it equals 71*1021, so no multiples of 71 or 1021 are in this sequence.)

Examples

			k       k^2 + k + 72491
0       72491 = 71*1021
1       72493 (prime)
2       72497 (prime)
3       72503 (prime)
4       72511 = 59*1229
5       72521 = 47*1543
6       72533 (prime)
7       72547 (prime)
8       72563 = 149*487
9       72581 = 181*401
etc.
		

Links

• Eric Chen, Table of n, a(n) for n = 1..4534 (all terms up to 10000)
• C. Rivera, Prime producing polynomials
• Eric Weisstein's World of Mathematics, Prime-generating polynomial

Crossrefs

Cf. A048097, A028823, A056561, A141489, A160548, A116206, A050267, A128878.

Programs

Magma

[n: n in [0..100] | IsPrime(n^2 + n + 72491)]; // Vincenzo Librandi, Apr 20 2015

Maple

select(t -> isprime(t^2+t+72491), [$0..100]);

Mathematica

Select[Range[100], PrimeQ[#^2 + # + 72491] &]

PARI

v=[ ]; for(n=0, 100, if(isprime(n^2+n+72491), v=concat(v, n), )); v