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%I A193558 #19 Dec 04 2020 15:01:44
%S A193558 3,12,20,64,96,60,144,176,100,620,304,1316,220,1220,1120,1580,1044,
%T A193558 736,3264,1356,944,976,500,1024,1056,3360,1184,1836,1264,3300,2076,
%U A193558 1424,1456,7760,820,1664,6076,2724,2796,1904,4900,3036,2064,2096,3204,5500,2256
%N A193558 Differences between consecutive primes of the form k^2+1.
%C A193558 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 A193558 Amiram Eldar, <a href="/A193558/b193558.txt">Table of n, a(n) for n = 1..10000</a>
%e A193558 a(2) = 12 because (4^2+1)-(2^2+1) = 17 - 5 = 12.
%t A193558 Differences[Select[Range[250]^2 + 1, PrimeQ]]
%o A193558 (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 A193558 Cf. A002496.
%K A193558 nonn
%O A193558 1,1
%A A193558 _Michel Lagneau_, Jul 30 2011

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