A253142 -id:A253142 - cp's OEIS frontend

A252783 Numbers n such that n + 15, n^2 + 15, n^3 + 15, n^4 + 15, n^5 + 15 and n^6 + 15 are all prime.

2, 4, 10830278, 11409622, 37189336, 41206834, 44438468, 65401492, 67135342, 85329104, 92243452, 110149004, 138651242, 182279216, 205680028, 216904744, 307575212, 309431906, 469311346, 490359076, 527228606, 529432582, 549804952, 572599934, 575037022, 596410214, 599921326, 616509454, 643063226, 679784492, 681657946, 722166524, 736641808, 766101998, 789147538, 824154506, 857134166, 870601984, 878365744, 914746816

Offset: 1

Zak Seidov, Dec 27 2014

nonn

			15 + {2, 4, 8, 16, 32, 64} = {17, 19, 23, 31, 47, 79} all primes.

Zak Seidov, Table of n, a(n) for n = 1..157

Cf. A253166, A253143, A253142, A086303, A121982.

isok(n) = isprime(n+15) && isprime(n^2 + 15) && isprime(n^3 + 15) && isprime(n^4 + 15) && isprime(n^5 + 15) && isprime(n^6 + 15); \\ Michel Marcus, Dec 28 2014

A253143 Numbers n such that n + 15, n^2 + 15 and n^3 + 15 are prime.

Original entry on oeis.org

2, 4, 16, 22, 32, 44, 86, 88, 98, 298, 316, 452, 602, 638, 658, 736, 862, 868, 896, 1276, 1358, 1586, 1768, 1996, 2342, 2366, 2444, 2452, 2542, 2788, 2902, 3242, 3448, 3704, 3718, 3998, 4376, 4552, 4928, 5422, 5504, 5566, 5608, 5644, 5728, 5768, 5776, 6664, 6934, 6946, 7708, 7858

Offset: 1

Zak Seidov, Dec 27 2014

nonn

			With n=2, n+15 (17), n^2+15 (19) and n^3+15 (23) are all prime.

Subsequence of A253142, A086303 and A121982.

p = 15; Select[Range[2, 20000, 2], PrimeQ[p + #^3] && PrimeQ[p + #^2] && PrimeQ[p + #] &]
Select[Range[2,8000,2],AllTrue[#^Range[3]+15,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 29 2018 *)

isok(n) = isprime(n+15) && isprime(n^2 + 15) && isprime(n^3 + 15); \\ Michel Marcus, Dec 28 2014

A253166 Numbers n such that n^k+15, with k=1..7, are all prime.

Original entry on oeis.org

599921326, 1107778868, 2011251698, 3589612642, 4811175086, 6153188512

Offset: 1

Zak Seidov, Dec 28 2014

No term (yet) with n^8 + 15 prime.

Subsequence of A252783.

Cf. A253143, A253142, A086303, A121982.

cp's OEIS Frontend

A252783 Numbers n such that n + 15, n^2 + 15, n^3 + 15, n^4 + 15, n^5 + 15 and n^6 + 15 are all prime.

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A253143 Numbers n such that n + 15, n^2 + 15 and n^3 + 15 are prime.

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PARI

A253166 Numbers n such that n^k+15, with k=1..7, are all prime.

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