A364707 a(n) is the least practical number A005153(k) such that A005153(k+1) - A005153(k) = 2*n, or -1 if no such number exists.
2, 8, 42, 112, 368, 180, 1806, 936, 840, 1600, 14168, 6216, 25120, 6272, 16770, 52668, 83720, 24240, 103840, 29440, 35910, 184140, 278334, 197912, 282150, 313040, 266112, 337840, 1438722, 468540, 1254016, 319808, 1486584, 2566432, 1321376, 2003688, 7163646, 3121328
Offset: 1
Keywords
Examples
a(1) = 2 since A005153(2) = 2 and A005153(3) = 4 = 2 + 2*1. a(2) = 8 since A005153(5) = 8 and A005153(6) = 12 = 8 + 2*2. a(3) = 42 since A005153(16) = 42 and A005153(17) = 48 = 42 + 2*3.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..150
Programs
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Mathematica
f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[n_] := (ind = Position[(fct = FactorInteger[n])[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most @ fct]), _?(# > 1 &)]) == {}; seq[len_, nmax_] := Module[{s = Table[0, {len}], n = 2, prev = 2, c = 0, i}, While[c < len && n <= nmax, n+=2; If[pracQ[n], i = (n - prev)/2; If[i <= len && s[[i]] == 0, c++; s[[i]] = prev]; prev= n]]; s]; seq[20, 10^6]