A334882 Numbers k such that k and k+2 are both primitive practical numbers (A267124).

28, 304, 306, 340, 460, 462, 858, 868, 1482, 1768, 1974, 2440, 2728, 2838, 2860, 3318, 3738, 4134, 4264, 4288, 4420, 4422, 5236, 5694, 6100, 6102, 7590, 8814, 9040, 9042, 10218, 11128, 11620, 11778, 12558, 12978, 13110, 14320, 14382, 14670, 15568, 16048, 16110

Offset: 1

Author

Amiram Eldar, May 14 2020

Keywords

• nonn

Examples

			28 is a term since 28 and 28 + 2 = 30 are both primitive practical numbers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A267124, A287681, A334883.

Programs

Mathematica

f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[fct_] := (ind = Position[fct[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most@fct]), ?(# > 1 &)]) == {}; pracTestQ[fct, k_] := Module[{f = fct}, f[[k, 2]] -= 1; pracQ[f]]; primPracQ[n_] := Module[{fct = FactorInteger[n]}, pracQ[fct] && AllTrue[Range@Length[fct], fct[[#, 2]] == 1 || ! pracTestQ[fct, #] &]]; Select[Range[2, 16200, 2], primPracQ[#] && primPracQ[# + 2] &]