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%I A253632 #14 Oct 06 2019 09:51:07
%S A253632 11,639517,730157,822763,1417159,1536047,1589443,1649677,2293771,
%T A253632 2410627,3427783,5773819,7171019,7224281,7398763,15467393,16844353,
%U A253632 17343839,20922043,21574387,22755203,23531407,23674891,25713101,25924733,28416277,32666047,37184561
%N 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.
%C A253632 Alternatively: Primes p such that p + 30*2^k is also prime at least for k = 0...6.
%C A253632 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.
%H A253632 K. D. Bajpai, <a href="/A253632/b253632.txt">Table of n, a(n) for n = 1..640</a>
%e A253632 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.
%e A253632 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.
%t A253632 Select[d = 30; Prime[Range[5000000]], PrimeQ[#+d] && PrimeQ[#+2d] && PrimeQ[#+4d] && PrimeQ[#+8d] && PrimeQ[#+16d] && PrimeQ[#+32d] && PrimeQ[#+64d] &]
%t A253632 Select[k = {0, 1, 2, 3, 4, 5, 6}; Prime[Range[5000000]], And @@ PrimeQ[# + 30*2^k] &]
%t A253632 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 *)
%o A253632 (PARI) forprime(p=1, 3e7, c=1; for(k=0, 6, if(!isprime(p+30*2^k), c--; break)); if(c, print1(p, ", ")))
%Y A253632 Cf. A000040, A000079.
%K A253632 nonn
%O A253632 1,1
%A A253632 _K. D. Bajpai_, Jan 06 2015

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