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Search: id:A109315
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| A109315 |
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Numbers n such that prime(n) - n is a prime power. |
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+0
1
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| 12, 15, 38, 39, 118, 152, 190, 258, 462, 690, 746, 1396, 1632, 2119, 3370, 4522, 4600, 7520, 15006, 24222, 33156, 34038, 51372, 52342, 64638, 77470, 90790, 101946, 104670, 156772, 166822, 167700, 175818, 194092, 200022, 229630, 246208, 328462
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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prime(n) - n = q^k, q is prime, and k_Integer >= 2.
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EXAMPLE
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690 is OK because prime(690)-690=5179-690=4489=672, 67 is prime.
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MATHEMATICA
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lst = {}; fQ[n_] := Block[{pf=FactorInteger[n]}, (2-Length[pf])(pf[[1, 2]]-1) > 0]; Do[ If[ fQ[Prime[n] - n], Print[n]; AppendTo[lst, n]], {n, 3, 362439}]; lst
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CROSSREFS
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Cf. A025475 = powers of a prime but not prime, also nonprime n such that sigma(n)*phi(n)>(n-1)2; A107712 = values of q, A107713 = values of k; A107714 = values of prime(A109315(n)).
Sequence in context: A134221 A065150 A087098 this_sequence A024875 A079322 A135451
Adjacent sequences: A109312 A109313 A109314 this_sequence A109316 A109317 A109318
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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), May 22 2005
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