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%I #12 Jan 16 2023 16:31:48
%S 5,17,197,577,2917,15377,41617,147457,215297,401957,414737,509797,
%T 1196837,1308737,1378277,1547537,1623077,1726597,1887877,2446097,
%U 2604997,2802277,2835857,3857297,4218917,4343057,4384837,5779217,6022117,6421157,7096897,8031557
%N Primes of the form n^2+1 such that (n+2)^2+1 is also prime.
%C Primes corresponding to A096012 and subset of A002496.
%C For n > 1, a(n) ==7 (mod 10) because n ==4 (mod 10).
%C Conjecture: this sequence is infinite.
%H Harvey P. Dale, <a href="/A206328/b206328.txt">Table of n, a(n) for n = 1..1000</a>
%e For n = 4, n^2 + 1 = 17 is prime and (n+2)^2 + 1 = 37 is also prime => 17 is in the sequence.
%p for n from 1 to 4000 do: x:=n^2+1:y:=(n+2)^2+1:if type(x,prime)=true and type(y,prime)=true then printf(`%d, `,x): else fi:od:
%t Select[Partition[Range[3000]^2+1,3,1],AllTrue[{#[[1]],#[[3]]},PrimeQ]&][[All,1]] (* _Harvey P. Dale_, Jan 16 2023 *)
%Y Cf. A096012, A002496.
%K nonn,easy
%O 1,1
%A _Michel Lagneau_, Feb 06 2012