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

1,1

Links

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

Example

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

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] &]

Crossrefs

Cf. A267124, A287681, A334883.

Sequence in context: A156711 A107942 A219172 * A196513 A042520 A022688

Adjacent sequences: A334879 A334880 A334881 * A334883 A334884 A334885

Keyword

nonn

Author

Amiram Eldar, May 14 2020

Status

approved