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

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Formula

prime(n) - n = q^k, q is prime and k_Integer >= 2.

Example

690 is OK because prime(690)-690 = 5179-690 = 4489 = 67^2, 67 is prime.

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

Crossrefs

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)).

Cf. A083240.

Sequence in context: A365850 A277082 A087098 * A024875 A152190 A330367

Adjacent sequences: A109312 A109313 A109314 * A109316 A109317 A109318

Keyword

nonn

Author

Zak Seidov and Robert G. Wilson v, May 22 2005

Status

approved