A316934 Primes p such that q^2 - p^2 + 1 is the square of a composite number where p and q are consecutive primes.

409, 599, 739, 911, 1217, 1481, 3539, 3637, 4421, 5081, 7591, 7951, 10301, 10993, 11173, 14449, 14533, 15619, 16073, 16453, 17203, 17341, 18661, 21319, 22259, 23671, 23869, 26267, 27059, 30169, 32119, 33409, 35531, 37139, 39511, 41411, 42193, 42641, 45979, 46171, 47741, 55931, 58937, 60761, 65089, 70991, 79867, 80599, 84389, 86579, 90523, 96739, 98909, 100913, 104717, 105199, 108343, 112573, 122263, 123551, 129581, 136951, 156419

Offset

1,1

Comments

Calculations provided by Robert Israel.

For what p will the number of squared prime be less than the number of squared composites? What would the distribution be for increasing p?

Links

Table of n, a(n) for n=1..63.

Example

With p=409 and q=419, 419^2 - 409^2 + 1 = 8281 = 91^2.

Mathematica

Select[Partition[Prime@ Range[10^4], 2, 1], CompositeQ@ Sqrt[#2^2 - #1^2 + 1] & @@ # &][[All, 1]] (* Michael De Vlieger, Jul 19 2018 *)

Crossrefs

Cf. A000040, A157750.

Sequence in context: A345797 A139661 A212604 * A052354 A213079 A260173

Adjacent sequences: A316931 A316932 A316933 * A316935 A316936 A316937

Keyword

nonn

Author

J. M. Bergot, Jul 16 2018

Status

approved