A182474 Primes of the form p^q - q, where p and q are primes.

2, 5, 7, 23, 47, 167, 359, 839, 1367, 1847, 2207, 3719, 5039, 7919, 8179, 10607, 11447, 16127, 17159, 19319, 29927, 36479, 44519, 49727, 54287, 57119, 66047, 85847, 97967, 113567, 128879, 177239, 196247, 201599, 218087, 241079, 273527, 292679, 323759, 344567

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Formula

Union of A049002 and A057678.

Example

8179 = 2^13 - 13

Mathematica

nn = 600000; mx = Floor[Log[2, nn]]; t2 = Select[Table[2^n - n, {n, Prime[Range[PrimePi[mx]]]}], PrimeQ]; mx = Floor[Sqrt[nn]]; tp = Select[Table[n^2 - 2, {n, Prime[Range[PrimePi[mx]]]}], PrimeQ]; Union[t2, tp] (* T. D. Noe, May 01 2012 *)
Module[{upto=350000, r}, r=Floor[Sqrt[upto+2]]; Select[Union[Select[ (#1[[1]]^#1[[2]]-#1[[2]]&)/@Tuples[Prime[Range[r]], 2], PrimeQ]], #1<=upto&]] (* Harvey P. Dale, Dec 07 2012 *)

Crossrefs

Cf. A049002 (primes of the form p^2 - 2).

Cf. A057678 (primes of the form 2^p - p).

Sequence in context: A243595 A103807 A099228 * A106018 A188499 A215535

Adjacent sequences: A182471 A182472 A182473 * A182475 A182476 A182477

Keyword

nonn,easy

Author

Alex Ratushnyak, May 01 2012

Status

approved