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

1,2

Links

Table of n, a(n) for n=1..6.

Example

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.

Mathematica

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]];

Crossrefs

Cf. A025475.

Sequence in context: A347721 A154131 A132554 * A059903 A227540 A353701

Adjacent sequences: A077272 A077273 A077274 * A077276 A077277 A077278

Keyword

more,nonn

Author

Robert G. Wilson v, Oct 31 2002

Extensions

a(6) from Donovan Johnson, Jun 19 2008

Status

approved