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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..27.

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 prime.

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;

CROSSREFS

Cf. A120806, A120807.

Sequence in context: A193436 A193501 A133990 * A092204 A079874 A186664

Adjacent sequences:  A120805 A120806 A120807 * A120809 A120810 A120811

KEYWORD

nonn

AUTHOR

Walter Kehowski, Jul 06 2006

STATUS

approved

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Last modified September 25 16:31 EDT 2017. Contains 292499 sequences.