A281437 Primes of the form 25*n^2 + 25*n + 47.

47, 97, 197, 347, 547, 797, 1097, 1447, 1847, 2297, 2797, 3347, 3947, 4597, 5297, 6047, 8597, 9547, 11597, 12697, 17597, 18947, 20347, 23297, 24847, 28097, 31547, 33347, 37097, 39047, 41047, 45197, 49547, 51797, 61297, 66347, 68947, 71597, 74297, 77047, 79847

Offset

1,1

Comments

The first 16 terms correspond to n from 0 to 15, which makes 25*n^2 + 25*n + 47 a prime-generating polynomial (see the link).

This is a prime-generating polynomial of the form s*n^2 + s*n + p, where s=k^2 and p is prime with s and p containing at most two digits. Prime-generating polynomials of this kind arise for k=1,2,3,5,7. This is the case of k=5; it generates most primes in a row out of the prime k's listed, with 12 for k=3,7, and 14 for k=2. See also A005846 and A007635 (k=1), and A048988 (k=2).

All terms are of the form 10m+7, with their next-to-last digits being 4 or 9.

Links

Table of n, a(n) for n=1..41.

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Example

197 is a term as it is a prime corresponding to n=2: 25*4 + 25*2 + 47 = 197.

Mathematica

Select[Range[0, 100]//25#^2+25#+47&, PrimeQ]

Prog

(PARI) for(n=0, 100, isprime(p=25*n^2+25*n+47)&& print1(p ", "))

Crossrefs

Cf. A000040 (primes), A005846, A007635, A048988, A292578 (similar prime-generating sequences).

Sequence in context: A044566 A349231 A141944 * A319051 A180550 A176134

Adjacent sequences: A281434 A281435 A281436 * A281438 A281439 A281440

Keyword

nonn

Author

Waldemar Puszkarz, Oct 05 2017

Status

approved