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Search: id:A076047
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| A076047 |
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Primes which are the difference between two successive nontrivial prime powers (A025475). |
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2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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 (wasserma(AT)spawar.navy.mil), Mar 31 2005
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EXAMPLE
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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.
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A025475, A053810, A075308.
Sequence in context: A028865 A053435 A096478 this_sequence A077316 A082011 A101044
Adjacent sequences: A076044 A076045 A076046 this_sequence A076048 A076049 A076050
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 29 2002
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 31 2005
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