login
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.
4
1, 5, 71, 303839, 1030349, 1356899, 1437719, 2248529, 2416259, 2576549, 2797961, 4007321, 4353521, 4875491, 6137501, 6611441, 6698831, 6904421, 7821791, 8078981, 9221231, 9311279, 9500279, 10157309, 11251421, 11879939, 11957969, 12040751, 13906649, 15299021, 16043369
OFFSET
1,2
LINKS
FORMULA
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.
EXAMPLE
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.
MAPLE
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;
PROG
(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
CROSSREFS
Sequence in context: A193501 A133990 A326881 * A092204 A079874 A186664
KEYWORD
nonn
AUTHOR
Walter Kehowski, Jul 06 2006
EXTENSIONS
a(28)-a(31) from Amiram Eldar, Aug 05 2024
STATUS
approved