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A352580 Numbers k such that A001414(k)*A001414(k+1)+A001414(k)+A001414(k+1) is prime.

%I A352580 #7 Mar 23 2022 12:49:42
%S A352580 1,2,3,4,6,13,14,18,19,20,23,24,28,38,40,42,44,45,48,52,53,63,68,80,
%T A352580 81,83,87,88,89,90,91,94,95,99,106,107,109,112,118,121,122,123,133,
%U A352580 134,135,137,145,146,148,149,153,158,159,162,164,166,173,175,176,179,183,184,188,196,202,207,209
%N A352580 Numbers k such that A001414(k)*A001414(k+1)+A001414(k)+A001414(k+1) is prime.
%C A352580 Numbers k such that (A001414(k)+1)*(A001414(k+1)+1)-1 is prime.
%H A352580 Robert Israel, <a href="/A352580/b352580.txt">Table of n, a(n) for n = 1..10000</a>
%e A352580 a(5)=6 is a term because A001414(6) = 2+3 = 5, A001414(7) = 7, and 5*7+5+7 = 47 is prime.
%p A352580 spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
%p A352580 select(t -> isprime((spf(t)+1)*(spf(t+1)+1)-1), [$1..1000]);
%Y A352580 Cf. A001414.
%K A352580 nonn
%O A352580 1,2
%A A352580 _J. M. Bergot_ and _Robert Israel_, Mar 21 2022