A056907 -id:A056907 - cp's OEIS frontend

A056908 Numbers k such that 36k^2 + 36k + 13 is prime.

0, 2, 4, 5, 7, 9, 14, 19, 22, 24, 29, 30, 34, 40, 42, 44, 50, 59, 62, 70, 72, 74, 75, 79, 80, 82, 84, 95, 102, 110, 119, 125, 132, 135, 139, 149, 150, 157, 160, 165, 172, 180, 197, 199, 200, 209, 210, 212, 224, 225, 227, 229, 230, 232, 235, 240, 244, 249

Offset: 1

Henry Bottomley, Jul 07 2000

36*k^2 + 36*k + 13 = (6*k+3)^2 + 4, which is 4 more than a square.

			a(2)=4 since 36*4^2 + 36*4 + 13 = 733, which is prime (as well as being four more than a square).

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

This sequence and formula, together with A056907 and its formula, generate all primes of the form k^2+4, i.e., A005473.

Cf. A056900, A056902, A056904, A056906.

[n: n in [0..70]| IsPrime(36*n^2+36*n+13)]; // Vincenzo Librandi, Jul 14 2012

Select[Range[0,700],PrimeQ[36#^2+36#+13]&] (* Vincenzo Librandi, Jul 14 2012 *)

is(n)=isprime(36*n^2+36*n+13) \\ Charles R Greathouse IV, Mar 01 2017

A056910 Numbers k such that 36k^2 + 12k + 7 is prime (sorted by absolute values with negatives before positives).

Original entry on oeis.org

0, -1, -2, 3, 4, 5, -6, 10, -11, 13, -15, 15, 18, -22, 24, 25, 29, -31, 33, -37, -45, -55, 55, 59, -67, -72, 74, 80, -81, 85, -86, 88, -90, -95, 99, -101, -102, 108, -116, 118, -122, 129, -130, 143, 148, -151, -155, -157, 158, 159, -162, 164, 165

Offset: 0

Henry Bottomley, Jul 07 2000

sign

36*k^2 + 12*k + 7 = (6*k+1)^2 + 6, which is six more than a square.

			a(2)=-2 since 36*(-2)^2 + 12*(-2) + 7 = 127, which is prime (as well as being six more than a square).

This sequence and formula generate all primes of the form k^2+6, i.e., A056909. Except for the first term, none of the a(n) are a multiple of 7 and so the rest of this sequence is a subsequence of A047304. Cf. A056900, A056902, A056904, A056906, A056907, A056908.

a(n) = (-1 +- sqrt(A056909(n) - 6))/6, choosing +- to give an integer result for each n.

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A056908 Numbers k such that 36k^2 + 36k + 13 is prime.

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A056910 Numbers k such that 36k^2 + 12k + 7 is prime (sorted by absolute values with negatives before positives).

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cp's OEIS Frontend

A056908 Numbers k such that 36*k^2 + 36*k + 13 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A056910 Numbers k such that 36*k^2 + 12*k + 7 is prime (sorted by absolute values with negatives before positives).

Views

Author

Keywords

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Examples

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Formula

A056908 Numbers k such that 36k^2 + 36k + 13 is prime.

A056910 Numbers k such that 36k^2 + 12k + 7 is prime (sorted by absolute values with negatives before positives).