A049495
a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5.
Original entry on oeis.org
7, 37, 163, 9157, 9277, 15667, 53593, 56893, 111577, 135193, 137383, 142543, 305407, 467527, 470647, 476023, 480043, 527377, 607093, 671353, 761377, 817147, 885943, 891643, 904663, 1080073, 1116637, 1140847, 1172803, 1233523
Offset: 1
7, 7+4=11, 7+16=23, 7+64=71, 7+256=263, 7+1024=1031 are all primes; the smallest such a sextuple is {7,11,23,71,263,1031}.
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Select[Prime@ Range[10^5], Function[p, AllTrue[Range@ 5, PrimeQ[p + 4^#] &]]] (* Michael De Vlieger, Aug 09 2017 *)
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isok(n) = isprime(n) && isprime(n+4) && isprime(n+16) && isprime(n+64) && isprime(n+256) && isprime(n+1024); \\ Michel Marcus, Dec 22 2013
A049494
a(n) and a(n)+4^k are primes at least for k=1,2,3,4.
Original entry on oeis.org
7, 37, 163, 757, 967, 1303, 2293, 2377, 8677, 8803, 9157, 9277, 14827, 15667, 16417, 20113, 27763, 29863, 41953, 53593, 56527, 56893, 61027, 67153, 69763, 74827, 79333, 83203, 90007, 95467, 111577, 129277, 135193, 137383, 142543, 151783
Offset: 1
7,7+4=11,7+16=23,7+64=71,7+256=263 are all primes: it is the smallest such quintet.
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Select[Prime[Range[15000]],AllTrue[#+{4,16,64,256},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 22 2018 *)
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isok(n) = isprime(n) && isprime(n+4) && isprime(n+4^2) && isprime(n+4^3) && isprime(n+4^4); \\ Michel Marcus, Dec 31 2013
A049497
a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5,6,7.
Original entry on oeis.org
37, 163, 15667, 142543, 607093, 671353, 1457857, 2694157, 2979043, 4890307, 5772097, 6404773, 9139453, 10669003, 11170933, 11218747, 11905987, 13243063, 15130537, 18116473, 19433863, 21960577, 23524183, 25946083, 32380177, 45600157, 46960747, 51905137
Offset: 1
37, 37+4=41, 37+16=53, 37+64=101, 37+256=293, 37+1024=1061, 37+4096=4133, 37+16384=16421 are all primes; the smallest such a 8-chain of primes is {37,41,53,101,293,1061,4133,16421}.
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filter:= n -> andmap(isprime, [n,n+4,n+4^2,n+4^3,n+4^4,n+4^5,n+4^6,n+4^7]):
select(filter, [seq(i,i=7..10^7,6)]); #Robert Israel, Nov 11 2019
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isok(n) = isprime(n) && isprime(n+4) && isprime(n+16) && isprime(n+64) && isprime(n+256) && isprime(n+1024) && isprime(n+4096) && isprime(n+16384); \\ Michel Marcus, Dec 22 2013
A049496
a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5,6.
Original entry on oeis.org
37, 163, 15667, 53593, 142543, 305407, 607093, 671353, 904663, 1172803, 1233523, 1351837, 1378843, 1389217, 1457857, 1686133, 1842523, 1867783, 2451793, 2668213, 2694157, 2979043, 3095227, 4228723, 4890307, 5535853, 5772097, 5859613, 6404773, 6827503, 6933067
Offset: 1
37, 37+4=41, 37+16=53, 37+64=101, 37+256=293, 37+1024=1061, 37+4096=4133 are all primes; the smallest such a 7-chain is {37,41,53,101,293,1061,4133}.
A049498
a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5,6,7,8.
Original entry on oeis.org
163, 15667, 607093, 671353, 1457857, 5772097, 9139453, 11170933, 13243063, 18116473, 19433863, 21960577, 32380177, 52896517, 115831753, 154146133, 165609217, 191489677, 361241743, 394845313, 518774953, 613615423, 705676717, 742403797, 786242293, 945170293
Offset: 1
163, 163+4 = 167, 163+16 = 179, 163+64 = 227, 163+256 = 419, 163+1024 = 1187, 163+4096 = 4259, 163+16384 = 16547, 163+65536 = 65699 are all primes; the smallest such a 9-chain of primes is {163, 167, 178, 227, 419, 1187, 4259, 16547, 65699}
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With[{c=4^Range[8]},Select[Prime[Range[500000]],And@@PrimeQ[#+c]&]] (* Harvey P. Dale, May 22 2012 *)
Showing 1-5 of 5 results.