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A261558 Euclid numbers (A006862) of the form 3*(i*i + i*j + j*j + i + j) + 1 where i and j are integers.

%I A261558 #13 Feb 16 2025 08:33:26
%S A261558 7,31,211,2311,510511,6469693231,200560490131,304250263527211,
%T A261558 117288381359406970983271,7858321551080267055879091,
%U A261558 40729680599249024150621323471,232862364358497360900063316880507363071,279734996817854936178276161872067809674997231
%N A261558 Euclid numbers (A006862) of the form 3*(i*i + i*j + j*j + i + j) + 1 where i and j are integers.
%C A261558 Intersection of A006862 and A202822.
%H A261558 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EuclidNumber.html">Euclid Number</a>
%e A261558 a(1) = 7 because 7 = 2*3 + 1 = 3*(1^2 + 1*0 + 0^2 + 1 + 0) + 1.
%o A261558 (PARI) a(n) = prod(k=1, n, prime(k)) + 1;
%o A261558 isA(n) = if( n<1 || (n%3 == 0), 0, 0 != sumdiv( n, d, kronecker( -3, d)));
%o A261558 for(n=0, 30, if(isA(a(n)), print1(a(n), ", ")))
%Y A261558 Cf. A003136, A006862, A202822.
%K A261558 nonn
%O A261558 1,1
%A A261558 _Altug Alkan_, Nov 18 2015