A109315 Numbers n such that prime(n) - n is a prime power.
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, 362440, 372882
Offset: 1
Keywords
Examples
690 is OK because prime(690)-690 = 5179-690 = 4489 = 67^2, 67 is prime.
Links
- Donovan Johnson, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Mathematica
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
Formula
prime(n) - n = q^k, q is prime and k_Integer >= 2.