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A120808 Integers p such that x = p^3 is in A120806: x+d+1 is prime for all divisors d of x. All p greater than 1 are odd primes.

%I A120808 #13 Aug 05 2024 04:38:41
%S A120808 1,5,71,303839,1030349,1356899,1437719,2248529,2416259,2576549,
%T A120808 2797961,4007321,4353521,4875491,6137501,6611441,6698831,6904421,
%U A120808 7821791,8078981,9221231,9311279,9500279,10157309,11251421,11879939,11957969,12040751,13906649,15299021,16043369
%N A120808 Integers p such that x = p^3 is in A120806: x+d+1 is prime for all divisors d of x. All p greater than 1 are odd primes.
%H A120808 Amiram Eldar, <a href="/A120808/b120808.txt">Table of n, a(n) for n = 1..2500</a>
%F A120808 a(1) = 1. a(n) = p where p is the (n-1)-st prime such that x = p^3 is in A120806: x+d+1 is prime for all divisors d of x.
%e A120808 a(3) = 71 since x = 71^3 = 357911, divisors(x) = {1, 71, 71^2, 71^3} and x+d+1 = {357913, 357983, 362953, 715823} are all primes.
%p A120808 L:=[]: for w to 1 do for k from 1 while nops(L)<=50 do p:=ithprime(k); x:=p^3; if p mod 6 = 5 and andmap(isprime,[x+2,2*x+1]) then S:={p,p^2}; Q:=map(z-> x+z+1, S); if andmap(isprime,Q) then L:=[op(L),x]; print(nops(L),p,x); fi; fi; od od;
%o A120808 (PARI) is(k) = {my(x=k^3); k == 1 || (isprime(k) && isprime(x+2) && isprime(x+k+1) && isprime(x+k^2+1) && isprime(2*x+1));} \\ _Amiram Eldar_, Aug 05 2024
%Y A120808 Cf. A120806, A120807.
%K A120808 nonn
%O A120808 1,2
%A A120808 _Walter Kehowski_, Jul 06 2006
%E A120808 a(28)-a(31) from _Amiram Eldar_, Aug 05 2024