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A193558 Differences between consecutive primes of the form k^2+1. 6

%I

%S 3,12,20,64,96,60,144,176,100,620,304,1316,220,1220,1120,1580,1044,

%T 736,3264,1356,944,976,500,1024,1056,3360,1184,1836,1264,3300,2076,

%U 1424,1456,7760,820,1664,6076,2724,2796,1904,4900,3036,2064,2096,3204,5500,2256

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

%C 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, ...}.

%H Amiram Eldar, <a href="/A193558/b193558.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (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

%Y Cf. A002496.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jul 30 2011

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Last modified January 27 21:49 EST 2023. Contains 359849 sequences. (Running on oeis4.)