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A352581 Numbers k such that A001414(k+1) = A001414(k)+1 and A001414(k)^2+3*A001414(k)+1 is prime.

%I A352581 #7 Mar 23 2022 17:34:37
%S A352581 2,3,4,20,24,1104,1274,2079,4345,13775,14905,20220,23408,25592,35167,
%T A352581 49230,61456,66585,68479,75648,76640,121539,172255,194403,200384,
%U A352581 229581,233090,236282,238017,247475,263145,283590,287615,295274,295640,326451,386169,422065,429385,429802,475968,585310
%N A352581 Numbers k such that A001414(k+1) = A001414(k)+1 and A001414(k)^2+3*A001414(k)+1 is prime.
%C A352581 Numbers k such that A001414(k+1) = A001414(k)+1 and (A001414(k)+1)*(A001414(k+1)+1)-1 is prime.
%H A352581 Robert Israel, <a href="/A352581/b352581.txt">Table of n, a(n) for n = 1..1000</a>
%e A352581 a(4) = 20 is a term because A001414(20) = 9, A001414(21) = 10 = 9+1, and 10*11-1 = 109 is prime.
%p A352581 spf:= proc(n) local t; option remember; add(t[1]*t[2], t=ifactors(n)[2]) end proc:
%p A352581 select(t -> (spf(t+1) = spf(t)+1) and isprime(spf(t)^2 + 3*spf(t)+1), [$1..10^6]);
%Y A352581 Intersection of A228126 and A352580. Cf. A001414.
%K A352581 nonn
%O A352581 1,1
%A A352581 _J. M. Bergot_ and _Robert Israel_, Mar 21 2022