A088259 Perfect powers which have at least one prime neighbor.

1, 4, 8, 16, 32, 36, 100, 128, 196, 256, 400, 576, 676, 1296, 1600, 2916, 3136, 4356, 5476, 7056, 8100, 8192, 8836, 12100, 13456, 14400, 15376, 15876, 16900, 17956, 21316, 22500, 24336, 25600, 28900, 30976, 32400, 33856, 41616, 42436, 44100

Offset: 1

Author

Amarnath Murthy, Sep 27 2003

Keywords

• nonn

Comments

If K is a term and K-1 is the neighboring prime then it must be a Mersenne prime.

Conjecture: sequence is infinite.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..322 (all terms up to 10 million)

Crossrefs

Intersection of A001597 and A045718.

Cf. A088256, A088257, A088258.

Programs

Mathematica

Join[{1},Select[Range[45000],GCD@@FactorInteger[#][[All,2]]>1 && AnyTrue[ #+{1,-1},PrimeQ]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 05 2020 *)

Extensions

Corrected and extended by Ray Chandler, Sep 28 2003

Offset changed by Andrew Howroyd, Sep 22 2024