A212908 Numbers n such that A212813(n) = 3.

13, 15, 16, 18, 19, 21, 22, 23, 25, 30, 32, 34, 36, 47, 53, 56, 63, 69, 74, 75, 76, 80, 90, 92, 96, 104, 108, 117, 123, 133, 136, 153, 165, 169, 172, 176, 190, 198, 228, 238, 245, 259, 273, 285, 286, 294, 304, 325, 328, 340, 342, 350, 357, 369, 370, 376, 385, 390, 403, 408, 416, 420, 423, 425, 429, 444, 448, 459, 462, 465, 468, 484, 496, 500

Offset: 1

Author

N. J. A. Sloane, May 30 2012

Keywords

• nonn
• fini
• full

References

• Bellamy, O. S.; Cadogan, C. C. Subsets of positive integers: their cardinality and maximality properties. Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1979), pp. 167--178, Congress. Numer., XXIII-XXIV, Utilitas Math., Winnipeg, Man., 1979. MR0561043 (82b:10006)

Links

• Reinhard Zumkeller and Donovan Johnson, Table of n, a(n) for n = 1..2632 (terms up to a(2500) from Reinhard Zumkeller)

Crossrefs

Cf. A212813, A212814, A212815, A212816, A212909.

Programs

Haskell

import Data.List (elemIndices)
a212908 n = a212908_list !! (n-1)
a212908_list = map (+ 1) $ elemIndices 3 a212813_list
-- Reinhard Zumkeller, May 30 2012

Mathematica

nmax = 258280326 (* = last term = a(2632) *);
kmax = 100 (* = number of terms to compute *);
a36288[n_] := a36288[n] = If[n==1, 1, Total[Times @@@ FactorInteger[n]]+1];
a212813[n_] := Module[{i, k = n}, For[i = 1, i <= 4, i++, If[k == 8, Return[i-1]]; k = a36288[k]]; -1];
k = 0;
Do[If[a212813[n] == 3, k++; If[k > kmax, Break[]]; a[k] = n; Print["a(", k, ") = ", n]], {n, 1, nmax}];
Array[a, kmax] (* Jean-François Alcover, Aug 02 2018 *)

Extensions

Keyword "full" added by Donovan Johnson, Jun 02 2012