

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
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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



