A120432 Numbers n such that n-1 and n+1 are prime powers.

2, 3, 4, 6, 8, 10, 12, 18, 24, 26, 28, 30, 42, 48, 60, 72, 80, 82, 102, 108, 126, 138, 150, 168, 180, 192, 198, 228, 240, 242, 270, 282, 312, 348, 360, 420, 432, 462, 522, 570, 600, 618, 642, 660, 728, 810, 822, 828, 840, 858, 882, 1020, 1032, 1050, 1062, 1092

Offset

1,1

Comments

A generalization of A014574.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

{2} UNION A088071. - R. J. Mathar, Aug 07 2008

Example

10 is in the sequence because both 9 and 11 are prime powers; 26 is in the sequence because both 25 and 27 are prime powers.

Maple

with(numtheory): a:=proc(n) if nops(factorset(n-1))*nops(factorset(n+1))=1 then n else fi end: 2, seq(a(n), n=2..1500); # Emeric Deutsch, Jul 23 2006

Mathematica

Insert[Select[Range[3, 3000], Length[FactorInteger[ # - 1]] == Length[ FactorInteger[ # + 1]] == 1 &], 2, 1] (* Stefan Steinerberger, Jul 23 2006 *)
Join[{2}, Select[Range[1100], And @@ PrimePowerQ /@ {# - 1, # + 1} &]] (* Ivan Neretin, Nov 24 2016 *)

Prog

(Magma) [2] cat [n : n in [3..1110] | IsPrimePower(n-1) and  IsPrimePower(n+1)]; // Vincenzo Librandi, Nov 25 2016

Crossrefs

Cf. A000961, A014574.

Sequence in context: A034287 A067128 A245779 * A020490 A217660 A275581

Adjacent sequences: A120429 A120430 A120431 * A120433 A120434 A120435

Keyword

nonn

Author

Greg Huber, Jul 13 2006

Extensions

More terms from Emeric Deutsch, Stefan Steinerberger and Ryan Propper, Jul 23 2006

Status

approved