A077273 -id:A077273 - cp's OEIS frontend

A077275 Least number which can be represented by the difference between two successive powers of a prime but not a prime (A077273) in just n ways.

1, 4, 17, 801528, 187117320, 17036037480

Offset: 1

Robert G. Wilson v, Oct 31 2002

			1 = 9-8, 4 = 8-4 & 125-121, 17 = 49 - 32 = 81 -64 = 529 - 512, 801528 = 1115760409 - 1114958881 = 4461839209 - 4461037681 = 10038637249 - 10037835721 = 40153346689 - 40152545161 and
187117320 = 9725896737769 - 9725709620449 = 21883150711249 - 21882963593929 = 60786363426721 - 60786176309401 = 243145173030769 - 243144985913449 = 2188305808807561 - 2188305621690241.

Cf. A025475.

pp = Sort[ Flatten[ Table[ Prime[n]^i, {n, 1, PrimePi[ Sqrt[10^16]]}, {i, 1, Log[ Prime[n], 10^16]}]]]; l = Length[pp]; b = Sort[ Take[pp, -l + 1] - Take[pp, l - 1]];

a(6) from Donovan Johnson, Jun 19 2008

A073652 Primes which occur as the difference of consecutive prime powers >1 as and when they occur.

Original entry on oeis.org

7, 2, 5, 17, 17, 3, 41, 13, 151, 17, 307, 199, 139, 271, 1217, 7, 751, 3617, 4241, 3343, 4001, 97169, 40841, 117017, 746153, 203897, 137542193, 256534591, 123090449

Offset: 1

Amarnath Murthy, Aug 10 2002

nonn

Conjecture: Every prime is a member.

These are the prime terms of A053707 in the order that they are found. Odd primes will be found only when one of the consecutive powers is a power of 2.

			41 is a member with 41 = 13^2- 2^7.

Cf. A076047, A077273

t = {}; Do[If[! PrimeQ[n] && PrimePowerQ[n], AppendTo[t, n]], {n, 3000000}]; Select[Differences[t], PrimeQ] (* Jayanta Basu, Jul 04 2013 *)

Corrected, extended, and edited by T. D. Noe, Apr 12 2009

cp's OEIS Frontend

A077275 Least number which can be represented by the difference between two successive powers of a prime but not a prime (A077273) in just n ways.

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