A200648 Length of Stolarsky representation of n.

1, 1, 2, 2, 3, 3, 3, 4, 3, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5, 5, 6, 4, 5, 5, 5, 6, 5, 5, 6, 5, 6, 6, 6, 7, 5, 5, 6, 5, 6, 6, 6, 7, 5, 6, 6, 6, 7, 6, 6, 7, 6, 7, 7, 7, 8, 5, 6, 6, 6, 7, 6, 6, 7, 6, 7, 7, 7, 8, 6, 6, 7, 6, 7, 7, 7, 8, 6, 7, 7, 7, 8, 7, 7, 8, 7, 8, 8

Offset

1,3

Comments

For the Stolarsky representation of n, see the C. Mongoven link.

Links

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

Casey Mongoven, Description of Stolarsky Representations.

Formula

a(n) = A200649(n) + A200650(n). - Michel Marcus, Mar 14 2023

Example

The Stolarsky representation of 19 is 11101. This is of length 5. So a(19) = 5.

Mathematica

stol[n_] := stol[n] = If[n == 1, {}, If[n != Round[Round[n/GoldenRatio]*GoldenRatio], Join[stol[Floor[n/GoldenRatio^2] + 1], {0}], Join[stol[Round[n/GoldenRatio]], {1}]]];
a[n_] := If[n == 1, 1, Length[stol[n]]]; Array[a, 100] (* Amiram Eldar, Jul 07 2023 *)

Prog

(PARI) stol(n) = {my(phi=quadgen(5)); if(n==1, [], if(n != round(round(n/phi)*phi), concat(stol(floor(n/phi^2) + 1), [0]), concat(stol(round(n/phi)), [1]))); }
a(n) = if(n == 1, 1, #stol(n)); \\ Amiram Eldar, Jul 07 2023

Crossrefs

Cf. A135817, A200649, A200650, A200651.

Sequence in context: A062558 A072789 A126302 * A264982 A134674 A253894

Adjacent sequences: A200645 A200646 A200647 * A200649 A200650 A200651

Keyword

nonn,base

Author

Casey Mongoven, Nov 19 2011

Extensions

More terms from Amiram Eldar, Jul 07 2023

Status

approved