OFFSET
1,1
COMMENTS
Alternatively: Primes p such that p + 30*2^k is also prime at least for k = 0...6.
Conjecture: In the expression p + d*2^k for k = 0...6; 1 < p < 10^6, d = 30 is the smallest value of d to yield such sequence.
LINKS
K. D. Bajpai, Table of n, a(n) for n = 1..640
EXAMPLE
a(1) = 11: 11+30 = 41; 11+2*30 = 71; 11+4*30 = 131; 11+8*30 = 251; 11+16*30 = 491; 11+32*30 = 971; 11+64*30 = 1931; all are prime.
a(2) = 639517: 639517+30 = 639547; 639517+2*30 = 639577; 639517+4*30 = 639637; 639517+8*30 = 639757; 639517+16*30 = 639997; 639517+32*30 = 640477; 639517+64*30 = 641437; all are prime.
MATHEMATICA
Select[d = 30; Prime[Range[5000000]], PrimeQ[#+d] && PrimeQ[#+2d] && PrimeQ[#+4d] && PrimeQ[#+8d] && PrimeQ[#+16d] && PrimeQ[#+32d] && PrimeQ[#+64d] &]
Select[k = {0, 1, 2, 3, 4, 5, 6}; Prime[Range[5000000]], And @@ PrimeQ[# + 30*2^k] &]
Select[Prime[Range[2273000]], AllTrue[#+30*2^Range[0, 6], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 06 2019 *)
PROG
(PARI) forprime(p=1, 3e7, c=1; for(k=0, 6, if(!isprime(p+30*2^k), c--; break)); if(c, print1(p, ", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Jan 06 2015
STATUS
approved