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A173446 ((n+{0,1})-th prime-1)^2+1 are both primes.

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%I A173446 #8 Sep 29 2024 02:54:51
%S A173446 1,2,3,4,12,31,36,53,54,78,82,105,125,155,247,403,422,548,678,679,751,
%T A173446 769,784,798,809,829,845,899,1049,1148,1155,1312,1317,1423,1436,1490,
%U A173446 1616,1688,1935,1961,1990,1991,2071,2181,2198,2397,2437,2454,2463,2556
%N A173446 ((n+{0,1})-th prime-1)^2+1 are both primes.
%C A173446 Numbers n such that ((n+{0,1})-th prime-1)^2+1 are both primes.
%H A173446 Robert Israel, <a href="/A173446/b173446.txt">Table of n, a(n) for n = 1..10000</a>
%e A173446 a(1)=1 because ((1+0)-th prime-1)^2+1=2=prime and ((1+1)-th prime-1)^2+1=5=prime; a(2)=2 because ((2+0)-th prime-1)^2+1=5=prime and ((2+1)-th prime-1)^2+1=17=prime
%p A173446 P:= select(isprime,[2,seq(i,i=3..10^6,2)]):
%p A173446 J:= select(i -> isprime((P[i]-1)^2+1),{$1..nops(P)}):
%p A173446 sort(convert(J intersect map(`-`,J,1),list)); # _Robert Israel_, Sep 29 2024
%Y A173446 Cf. A000040, A006093, A127435, A173444.
%K A173446 nonn
%O A173446 1,2
%A A173446 _Juri-Stepan Gerasimov_, Feb 18 2010
%E A173446 126 removed. Terms beyond 247 added by _R. J. Mathar_, Mar 01 2010