A334883 Primitive practical numbers (A267124) with a record gap to the next primitive practical number.

1, 2, 6, 42, 104, 140, 1036, 1590, 2730, 7900, 10374, 19180, 22660, 23180, 26418, 105868, 114960, 139060, 295780, 403524, 482250, 1294144, 2468944, 4799058, 5379282, 19035500, 20233936, 21803860, 112406992, 789190976, 3520928922

Offset

1,2

Comments

The record gap values are 1, 4, 14, 24, 36, 64, 74, 82, 84, 104, 106, 112, 120, 132, 154, 188, 204, 224, 236, 246, 258, 308, 326, 360, 418, 440, 452, 508, 674, 804, 846, ...

Links

Table of n, a(n) for n=1..31.

Example

The first 8 primitive practical numbers are 1, 2, 6, 20, 28, 30, 42 and 66. The differences between these terms are 1, 4, 14, 8, 2, 12 and 24. The record gaps are 1, 4, 14 and 24, which occur after the terms 1, 2, 6 and 42.

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, #] &]]; seq = {1}; m = 2; dm = 1; Do[If[primPracQ[n], d = n - m; If[d > dm, dm = d; AppendTo[seq, m]]; m = n], {n, 4, 10^5, 2}]; seq

Crossrefs

Cf. A267124, A330870, A334882.

Sequence in context: A309813 A033936 A203618 * A098814 A272177 A346548

Adjacent sequences: A334880 A334881 A334882 * A334884 A334885 A334886

Keyword

nonn,more

Author

Amiram Eldar, May 14 2020

Status

approved