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

1,2

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.)

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

Example

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.

Maple

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

Mathematica

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

Prog

(PARI) v=[ ]; for(n=0, 100, if(isprime(n^2+n+72491), v=concat(v, n), )); v
(Magma) [n: n in [0..100] | IsPrime(n^2 + n + 72491)]; // Vincenzo Librandi, Apr 20 2015

Crossrefs

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

Sequence in context: A362286 A050031 A003421 * A226384 A298947 A075995

Adjacent sequences: A253236 A253237 A253238 * A253240 A253241 A253242

Keyword

nonn,easy

Author

Eric Chen, Apr 19 2015

Status

approved