A049495 -id:A049495 - cp's OEIS frontend

A049494 a(n) and a(n)+4^k are primes at least for k=1,2,3,4.

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

Labos Elemer

nonn

			7,7+4=11,7+16=23,7+64=71,7+256=263 are all primes: it is the smallest such quintet.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A023200, A049492, A049493, A049495-A049500.

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 *)

isok(n) = isprime(n) && isprime(n+4) && isprime(n+4^2) && isprime(n+4^3) && isprime(n+4^4); \\ Michel Marcus, Dec 31 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

Labos Elemer

nonn

			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}.

Cf. A023200, A049492-A049495, A049497-A049500.

isok(n) = isprime(n) && isprime(n+4) && isprime(n+16) && isprime(n+64) && isprime(n+256) && isprime(n+1024) && isprime(n+4096); \\ Michel Marcus, Dec 22 2013

A023200 INTERSECT A269259. - R. J. Mathar, Mar 26 2024

More terms from Michel Marcus, Dec 22 2013

A247590 Primes p such that p + 6^k is also prime at least for k = 1, 2, 3 and 4.

Original entry on oeis.org

7, 11, 23, 131, 157, 193, 227, 271, 331, 571, 947, 977, 1013, 1087, 1283, 1453, 1657, 1871, 2341, 2671, 2693, 3607, 3637, 3691, 4013, 4951, 5407, 5653, 6211, 6353, 6653, 6827, 6977, 6991, 7541, 7717, 8053, 8081, 8537, 9203, 9613, 9643, 10853, 11113, 11251, 11933

Offset: 1

K. D. Bajpai, Sep 20 2014

			a(1) = 7 is prime. 7 + 6^1 = 13, 7 + 6^2 = 43, 7 + 6^3 = 223 and 7 + 6^4 = 1303 are also prime. It is the smallest such set of 5 primes; (Quintet).

K. D. Bajpai, Table of n, a(n) for n = 1..12638

Cf. A000040, A049494, A049495.

Select[k = {1, 2, 3, 4}; Prime[Range[500]], And @@ PrimeQ[# + 6^k] &]

forprime(p=1,10^4,c=1;for(k=1,4,if(!isprime(p+6^k),c--;break));if(c,print1(p,", "))) \\ Derek Orr, Sep 20 2014

cp's OEIS Frontend

A049494 a(n) and a(n)+4^k are primes at least for k=1,2,3,4.

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A049496 a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5,6.

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Author

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PARI

Formula

Extensions

A247590 Primes p such that p + 6^k is also prime at least for k = 1, 2, 3 and 4.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI