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

1,4

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.

Example

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

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 *)

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

Crossrefs

Cf. A200647, A200648, A200649, A200650.

Sequence in context: A182321 A285731 A114905 * A126597 A261867 A076081

Adjacent sequences: A200648 A200649 A200650 * A200652 A200653 A200654

Keyword

nonn,base

Author

Casey Mongoven, Nov 19 2011

Extensions

More terms from Amiram Eldar, Jul 07 2023

Status

approved