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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..150

Formula

a(n) = A005153(A364706(n)).

Example

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.

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]

Crossrefs

Cf. A005153, A179651, A330870, A364706.

Sequence in context: A226458 A364383 A330870 * A342152 A153537 A153565

Adjacent sequences: A364704 A364705 A364706 * A364708 A364709 A364710

Keyword

nonn

Author

Amiram Eldar, Aug 04 2023

Status

approved