A352581 - OEIS

%I #7 Mar 23 2022 17:34:37

%S 2,3,4,20,24,1104,1274,2079,4345,13775,14905,20220,23408,25592,35167,

%T 49230,61456,66585,68479,75648,76640,121539,172255,194403,200384,

%U 229581,233090,236282,238017,247475,263145,283590,287615,295274,295640,326451,386169,422065,429385,429802,475968,585310

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

%C Numbers k such that A001414(k+1) = A001414(k)+1 and (A001414(k)+1)*(A001414(k+1)+1)-1 is prime.

%H Robert Israel, <a href="/A352581/b352581.txt">Table of n, a(n) for n = 1..1000</a>

%e a(4) = 20 is a term because A001414(20) = 9, A001414(21) = 10 = 9+1, and 10*11-1 = 109 is prime.

%p spf:= proc(n) local t; option remember; add(t[1]*t[2], t=ifactors(n)[2]) end proc:

%p select(t -> (spf(t+1) = spf(t)+1) and isprime(spf(t)^2 + 3*spf(t)+1), [$1..10^6]);

%Y Intersection of A228126 and A352580. Cf. A001414.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Mar 21 2022