A193558 Differences between consecutive primes of the form k^2+1.

3, 12, 20, 64, 96, 60, 144, 176, 100, 620, 304, 1316, 220, 1220, 1120, 1580, 1044, 736, 3264, 1356, 944, 976, 500, 1024, 1056, 3360, 1184, 1836, 1264, 3300, 2076, 1424, 1456, 7760, 820, 1664, 6076, 2724, 2796, 1904, 4900, 3036, 2064, 2096, 3204, 5500, 2256

Offset: 1

Author

Michel Lagneau, Jul 30 2011

Keywords

• nonn

Comments

It is conjectured that the sequence of primes of the form k^2+1 is infinite, but this has never been proved. This sequence contains a subset of squares: {64, 144, 100, 1024, 4900, 10816, 11664, 12544, 18496, 102400, 41616, ...}.

Examples

			a(2) = 12 because (4^2+1)-(2^2+1) = 17 - 5 = 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002496.

Programs

Mathematica

Differences[Select[Range[250]^2 + 1, PrimeQ]]

PARI

lista(nn) = my(v=select(x->issquare(x-1), primes(nn))); vector(#v-1, k, v[k+1] - v[k]) \\ Michel Marcus, Dec 04 2020