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A321795 Numbers m such that m^2+1 is prime with (m-1)^2+1 and (m+1)^2+1 semiprimes.

%I A321795 #11 Sep 04 2019 10:55:47
%S A321795 4,10,170,570,780,950,1420,2380,2730,3850,4120,4300,5850,6360,6460,
%T A321795 6800,6970,7100,7240,8720,9630,10150,10580,11010,11170,11830,12300,
%U A321795 14290,16330,17670,17810,17850,17860,18940,19030,20500,21930,23960,24490,25830,26050
%N A321795 Numbers m such that m^2+1 is prime with (m-1)^2+1 and (m+1)^2+1 semiprimes.
%C A321795 Subsequence of A005574.
%C A321795 For n>1, a(n) == 0 (mod 10).
%C A321795 The corresponding pairs of semiprimes ((m-1)^2+1, (m+1)^2+1) are of the form (2p, 2q) with p, q primes == 1 (mod 10). So, a(n) = (q - p)/2 and a(n)^2 + 1 = p + q - 1.
%H A321795 Harvey P. Dale, <a href="/A321795/b321795.txt">Table of n, a(n) for n = 1..1000</a>
%e A321795 10 is in the sequence because 10^2 + 1 = 101 is prime, and 9^2 + 1 = 2*41, 11^2 + 1 = 2*61 are semiprimes.
%t A321795 Select[Range[50000],PrimeOmega[(#-1)^2+1]==2&&PrimeQ[#^2+1]&&PrimeOmega[(#+1)^2+1]==2&]
%t A321795 Mean/@SequencePosition[Table[Which[PrimeQ[m^2+1],1,PrimeOmega[m^2+1]==2,2,True,0],{m,30000}],{2,1,2}] (* Requires Mathematica version 10 or later *)  (* _Harvey P. Dale_, Sep 04 2019 *)
%o A321795 (PARI) isok(m) = isprime(m^2+1) && (bigomega((m-1)^2+1) == 2) && (bigomega((m+1)^2+1) == 2); \\ _Michel Marcus_, Nov 20 2018
%Y A321795 Cf. A005574, A085722.
%K A321795 nonn
%O A321795 1,1
%A A321795 _Michel Lagneau_, Nov 19 2018