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A088259
Perfect powers which have at least one prime neighbor.
2
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
1,2
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)
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 *)
CROSSREFS
Intersection of A001597 and A045718.
Sequence in context: A322793 A377138 A283052 * A123857 A217313 A101434
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 27 2003
EXTENSIONS
Corrected and extended by Ray Chandler, Sep 28 2003
Offset changed by Andrew Howroyd, Sep 22 2024
STATUS
approved