cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A056907 Numbers k such that 36*k^2 + 12*k + 5 is prime (sorted by absolute values with negatives before positives).

Original entry on oeis.org

0, -1, 1, 2, -3, -6, 6, -8, -11, 11, 12, 14, -16, 16, 17, 19, -21, -23, -26, 27, -28, 32, -34, -36, 36, -39, 39, -41, 42, 44, -46, 46, -48, -49, 51, 52, -53, -58, 62, 64, 67, -68, -71, 71, -76, 77, 79, 81, -84, -89, 91, 96, -99, -101, 101, 102, -104, -111, 111, -113
Offset: 0

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Author

Henry Bottomley, Jul 07 2000

Keywords

Comments

36*k^2 + 12*k + 5 = (6*k+1)^2 + 4, which is four more than a square. Except for a(0), a(n) is never a multiple of 5.

Examples

			a(3)=2 since 36*2^2 + 12*2 + 5 = 173 which is prime (as well as being four more than a square).

Crossrefs

This sequence and formula, together with A056908 and its formula, generate all primes of the form k^2+4, i.e., A005473. Except for the first term, this sequence is a subsequence of A047201. Cf. A056900, A056902, A056904, A056906.

A056910 Numbers k such that 36*k^2 + 12*k + 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

Views

Author

Henry Bottomley, Jul 07 2000

Keywords

Comments

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

Examples

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

Crossrefs

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.

Formula

a(n) = (-1 +- sqrt(A056909(n) - 6))/6, choosing +- to give an integer result for each n.
Showing 1-2 of 2 results.

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