A253632 Primes p such that p+d, p+2d, p+4d, p+8d, p+16d, p+32d and p+64d are also primes for d = 30.

11, 639517, 730157, 822763, 1417159, 1536047, 1589443, 1649677, 2293771, 2410627, 3427783, 5773819, 7171019, 7224281, 7398763, 15467393, 16844353, 17343839, 20922043, 21574387, 22755203, 23531407, 23674891, 25713101, 25924733, 28416277, 32666047, 37184561

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

Cf. A000040, A000079.

Sequence in context: A320625 A219013 A243130 * A112854 A211238 A014127

Adjacent sequences: A253629 A253630 A253631 * A253633 A253634 A253635

Keyword

nonn

Author

K. D. Bajpai, Jan 06 2015

Status

approved