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A076047 Primes which are the difference between two successive nontrivial prime powers (A025475). 1
2, 3, 5, 7, 13, 17, 41, 139, 151, 199, 271, 307, 751, 1217, 3343, 3617, 4001, 4241, 40841, 97169, 117017, 203897, 746153, 123090449, 137542193, 256534591, 21249911167, 88109383889, 112332648583, 85726065193313, 226411321073393 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

I have searched through prime powers up to 2^8532. It is very unlikely that there are any other values between the ones listed here, but no prime has been proved to be absent from this sequence. - David Wasserman, Mar 31 2005

LINKS

Table of n, a(n) for n=1..31.

EXAMPLE

3 = 128 - 125 = 2^7 - 5^3; 7 = 16 - 9 = 32768 - 32761; 17 = 49 - 32 = 81 - 64 = 529 - 512; 4241 = 528529 - 524288 = 727^2 - 2^19.

MATHEMATICA

pp = Sort[ Flatten[ Table[ Prime[n]^i, {n, 1, PrimePi[ Sqrt[10^16]]}, {i, 1, Log[ Prime[n], 10^16]}]]]; l = Length[pp]; d = Sort[Take[pp, -l + 1] - Take[pp, l - 1]]; a = {}; Do[ If[ PrimeQ[ d[[n]]], a = Append[a, d[[n]]]], {n, 1, l - 1}]; Union[a] a = {}; Do[ If[ PrimeQ[ pp[[n + 1]] - pp[[n]]], a = Append[a, pp[[n + 1]] - pp[[n]]]], {n, 1, Length[pp] - 1}]; Union[a]

CROSSREFS

Cf. A025475, A053810, A075308.

Sequence in context: A028865 A053435 A096478 * A245640 A178766 A077316

Adjacent sequences:  A076044 A076045 A076046 * A076048 A076049 A076050

KEYWORD

nonn

AUTHOR

Zak Seidov and Robert G. Wilson v, Oct 29 2002

EXTENSIONS

More terms from David Wasserman, Mar 31 2005

STATUS

approved

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Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)