A200651 Number of equal bit-runs in Stolarsky Representation of n.

1, 1, 1, 2, 1, 3, 2, 1, 2, 3, 3, 2, 1, 4, 3, 3, 2, 3, 3, 2, 1, 2, 5, 3, 4, 3, 4, 3, 3, 2, 3, 3, 2, 1, 4, 3, 5, 4, 3, 5, 4, 3, 2, 5, 3, 4, 3, 4, 3, 3, 2, 3, 3, 2, 1, 2, 5, 3, 6, 5, 5, 4, 3, 4, 5, 5, 4, 3, 4, 3, 5, 4, 3, 5, 4, 3, 2, 5, 3, 4, 3, 4, 3, 3, 2, 3, 3

Offset: 1

Author

Casey Mongoven, Nov 19 2011

Keywords

• nonn
• base

Comments

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

Examples

			The Stolarsky representation of 19 is 11101. This has 3 equal bit-runs: '111', '0' and '1'. So a(19) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Casey Mongoven, Description of Stolarsky Representations.

Crossrefs

Cf. A200647, A200648, A200649, A200650.

Programs

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[Split[stol[n]]]]; Array[a, 100] (* Amiram Eldar, Jul 07 2023 *)

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) = {my(s = stol(n), c = 1); for(k = 1, #s-1, if(s[k+1] != s[k], c++)); c; } \\ Amiram Eldar, Jul 07 2023

Extensions

More terms from Amiram Eldar, Jul 07 2023