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 1-4 of 4 results.

A107605 Numbers n such that prime(n) + n is a perfect power.

Original entry on oeis.org

3, 5, 8, 9, 12, 86, 105, 147, 176, 214, 230, 241, 355, 412, 503, 696, 1065, 1147, 1170, 1273, 1334, 2021, 2455, 2600, 2660, 2772, 3299, 3332, 3365, 4417, 4861, 6288, 6478, 6572, 8115, 8858, 8905, 9229, 9380, 9590, 9692, 9749, 10501, 10829, 11338, 11633
Offset: 1

Views

Author

Zak Seidov, May 17 2005

Keywords

Examples

			Prime(8) + 8 = 19 + 8 = 27 = 3^3.

Crossrefs

Cf. A001597 (perfect powers), A107606 (associated prime(n)+n), A107607, A107608, A109314.

Programs

  • Mathematica
    f[n_] := Prime[n] + n; Select[Range[10^4], ! GCD @@ Last /@ FactorInteger[f[ # ]] == 1 &] (* Ray Chandler, May 21 2005 *)
  • Sage
    [n for n in (1..10000) if (n+nth_prime(n)).is_perfect_power()] # Giuseppe Coppoletta, Jun 08 2016

Extensions

Extended by Ray Chandler, May 21 2005

A107607 Numbers n such that prime(n) - n is a perfect power.

Original entry on oeis.org

1, 2, 12, 15, 38, 39, 100, 118, 152, 190, 212, 258, 352, 462, 542, 690, 741, 746, 1285, 1396, 1417, 1632, 2119, 2243, 2318, 2603, 3370, 3777, 4073, 4155, 4485, 4522, 4600, 4719, 5317, 5446, 6697, 6748, 6985, 7144, 7520, 7595, 9492, 9551, 12010, 12985
Offset: 1

Views

Author

Zak Seidov, May 17 2005

Keywords

Examples

			Prime(12) - 12 = 37 - 12 = 25 = 5^2.

Crossrefs

Cf. A001597 (perfect powers), A107605, A107606, A107608 (associated prime(n)-n).

Programs

  • Mathematica
    f[n_] := Prime[n] - n; Select[Range[10^4], ! GCD @@ Last /@ FactorInteger[f[ # ]] == 1 &] (* Ray Chandler, May 21 2005 *)
  • PARI
    isA107607(n)=(ispower(prime(n)-n) > 1) || (prime(n)-n == 1) \\ Michael B. Porter, Sep 28 2009

Extensions

Extended by Ray Chandler, May 21 2005

A107608 Perfect powers which have the form prime(n) - n for some n.

Original entry on oeis.org

1, 1, 25, 32, 125, 128, 441, 529, 729, 961, 1089, 1369, 2025, 2809, 3375, 4489, 4900, 4913, 9216, 10201, 10404, 12167, 16384, 17576, 18225, 20736, 27889, 31684, 34596, 35344, 38416, 38809, 39601, 40804, 46656, 47961, 60516, 61009, 63504, 65025
Offset: 1

Views

Author

Zak Seidov, May 17 2005

Keywords

Comments

Corresponding n's in A107607.

Crossrefs

Cf. A001597 (perfect powers), A107605, A107606, A107607 (associated n).

Programs

  • Mathematica
    f[n_] := Prime[n] - n; Select[f /@ Range[10^4], ! GCD @@ Last /@ FactorInteger[ # ] == 1 &] (* Ray Chandler, May 21 2005 *)

Formula

a(n) = prime(A107607(n)) - A107607(n).

Extensions

Extended by Ray Chandler, May 21 2005

A239280 Powers of 2 that are sum of prime(k) + k for some k.

Original entry on oeis.org

8, 16, 32, 4096
Offset: 1

Views

Author

Zak Seidov, Mar 14 2014

Keywords

Comments

a(5) > 2^47. - Giovanni Resta, Mar 14 2014
a(5) > 2^62 if it exists. - Chai Wah Wu, Apr 28 2018

Examples

			3 + prime(3) = 8 = 2^3.
5 + prime(5) = 16 = 2^4.
9 + prime(9) = 32 = 2^5.
503 + prime(503) = 4096 = 2^12.

Crossrefs

Cf. A014688, A064371, A073856, A107606.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.