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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. 3

%I

%S 1,5,71,303839,1030349,1356899,1437719,2248529,2416259,2576549,

%T 2797961,4007321,4353521,4875491,6137501,6611441,6698831,6904421,

%U 7821791,8078981,9221231,9311279,9500279,10157309,11251421,11879939,11957969

%N 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.

%F 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 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 prime.

%p 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;

%Y Cf. A120806, A120807.

%K nonn

%O 1,2

%A _Walter Kehowski_, Jul 06 2006

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Last modified November 28 01:24 EST 2021. Contains 349396 sequences. (Running on oeis4.)