cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A089559 Nonnegative numbers n such that 2*n + 15 is prime.

Original entry on oeis.org

1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 22, 23, 26, 28, 29, 32, 34, 37, 41, 43, 44, 46, 47, 49, 56, 58, 61, 62, 67, 68, 71, 74, 76, 79, 82, 83, 88, 89, 91, 92, 98, 104, 106, 107, 109, 112, 113, 118, 121, 124, 127, 128, 131, 133, 134, 139, 146, 148, 149, 151, 158, 161, 166
Offset: 1

Views

Author

Ray Chandler, Nov 29 2003

Keywords

Links

Crossrefs

Cf. A086303.
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), this seq (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

Programs

Formula

a(n) = A086303(n)/2.

Extensions

Definition clarified by Zak Seidov, Jul 11 2014

A253142 Numbers k such that k + 15 and k^2 + 15 are prime.

Original entry on oeis.org

2, 4, 8, 14, 16, 22, 26, 32, 38, 44, 46, 52, 64, 68, 86, 88, 98, 124, 134, 158, 178, 184, 196, 212, 236, 242, 248, 256, 262, 296, 298, 316, 322, 338, 364, 374, 386, 394, 452, 472, 484, 488, 548, 578, 586, 598, 602, 626, 632, 638, 646, 658, 662, 676, 694, 718, 728, 736, 794, 806, 842, 848, 862
Offset: 1

Views

Author

Zak Seidov, Dec 27 2014

Keywords

Examples

			2 + 15 = 17 and 2^2 + 15 = 19 are both prime, so 2 is in the sequence.

Links

Crossrefs

Intersection of A086303 and A121982.

Programs

  • Maple
    select(t -> isprime(t+15) and isprime(t^2+15), [seq(i,i=2..1000,2)]); # Robert Israel, May 07 2019
  • Mathematica
    p = 15; Select[Range[2,1000,2], PrimeQ[p + #^2] && PrimeQ[p + #] &]
Select[Range[2,1000,2],AllTrue[{#,#^2}+15,PrimeQ]&] (* Harvey P. Dale, Jun 08 2023 *)

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.

Original entry on oeis.org

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

Views

Author

Zak Seidov, Dec 27 2014

Keywords

Examples

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

Links

Crossrefs

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

Programs

  • PARI
    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

Views

Author

Zak Seidov, Dec 27 2014

Keywords

Examples

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

Crossrefs

Subsequence of A253142, A086303 and A121982.

Programs

  • Mathematica
    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 *)
  • PARI
    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

Views

Author

Zak Seidov, Dec 28 2014

Keywords

Comments

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

Crossrefs

Subsequence of A252783.
Cf. A253143, A253142, A086303, A121982.
Showing 1-5 of 5 results.

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