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A099742 Least number B such that (A001359(n)-B^2)^2+B is also the lesser of larger twin primes, or 0 if no such B exists.

%I A099742 #9 Dec 30 2019 10:05:26
%S A099742 1,1,1,7,412,7,7,133,7,7,316,7,25,10,10,10,7,7,16,10,7,25,1,7,7,100,
%T A099742 55,7,28,940,37,148,22,16,28,67,31,82,64,4,82,445,292,310,16,1687,13,
%U A099742 37,43,7,58,22,31,97,70,7,22,1,19,52,58,25,1,367,4,7,4,37,55
%N A099742 Least number B such that (A001359(n)-B^2)^2+B is also the lesser of larger twin primes, or 0 if no such B exists.
%C A099742 Conjecture: No term is zero.
%H A099742 Amiram Eldar, <a href="/A099742/b099742.txt">Table of n, a(n) for n = 1..10000</a>
%e A099742 a(3) = 1 since A001359(3) = 11, 11 & 13 are twin primes, (11 - 1^2)^2 + 1 = 101, and 101 & 103 are also twin primes.
%t A099742 f[p_] := Module[{b = 1}, While[(pb = (p - b^2)^2 + b) <= p || ! And @@ PrimeQ[pb + {0, 2}], b++]; b]; seq = {}; Do[If[And @@ PrimeQ[p + {0, 2}], AppendTo[seq, f[p]]], {p, 2, 3000}]; seq (* _Amiram Eldar_, Dec 30 2019 *)
%Y A099742 Cf. A001359, A099728.
%K A099742 nonn
%O A099742 1,4
%A A099742 _Ray G. Opao_, Nov 09 2004
%E A099742 More terms from _Amiram Eldar_, Dec 30 2019