A131565 Numbers n such that 3*n^2 + 5*n +1 is either a prime or a power of three multiplied with a prime.

2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 28, 30, 31, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 47, 51, 52, 53, 55, 56, 58, 59, 61, 64, 65, 66, 69, 72, 76, 79, 81, 82, 84, 86, 87, 91, 95, 98, 100, 102, 103, 104, 105, 107, 108, 109, 113, 115, 116, 118

Offset

1,1

Links

Table of n, a(n) for n=1..68.

Example

3*2^2 + 5*2 + 1 = 23, which is prime. Therefore 2 is in the sequence.
3*4^2 + 5*4 + 1 = 3*23, a prime multiplied by a power of 3. Hence 3 is in the sequence.

Mathematica

a = {}; For[n = 1, n < 130, n++, m = 3*n^2 + 5*n + 1; If[PrimeQ[m], AppendTo[a, n]]; While[IntegerQ[m/3], m = m/3]; If[PrimeQ[m], AppendTo[a, n]]]; Union[a, a]

Crossrefs

Sequence in context: A350425 A259627 A250475 * A039218 A076487 A317717

Adjacent sequences: A131562 A131563 A131564 * A131566 A131567 A131568

Keyword

nonn,less

Author

J. M. Bergot, Aug 27 2007

Extensions

Edited, corrected and extended by Stefan Steinerberger, Aug 29 2007

Status

approved