A200714 Stolarsky representation interpreted as binary to decimal integers.

0, 1, 3, 2, 7, 5, 6, 15, 4, 11, 13, 14, 31, 10, 9, 23, 12, 27, 29, 30, 63, 8, 21, 19, 22, 47, 26, 25, 55, 28, 59, 61, 62, 127, 20, 17, 43, 18, 39, 45, 46, 95, 24, 53, 51, 54, 111, 58, 57, 119, 60, 123, 125, 126, 255, 16, 41, 35, 42, 87, 37, 38, 79, 44, 91, 93

Offset

1,3

Comments

See explanation of Stolarsky representations in the C. Mongoven link.

Links

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

Casey Mongoven, Description of Stolarsky Representations.

Formula

From Amiram Eldar, Jul 07 2023: (Start)

A000120(a(n)) = A200649(n).

A023416(a(n)) = A200650(n).

A070939(a(n)) = A200648(n).

A005811(a(n)) = A200651(n). (End)

Conjecture: a(n) = A367306(A358654(n-1)). - Mikhail Kurkov, Oct 17 2024

Example

The Stolarsky representation of 19 is 11101. In binary this is equal to 29. So a(19) = 29.

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_] := FromDigits[stol[n], 2]; Array[a, 100] (* Amiram Eldar, Jul 07 2023 *)

Prog

(PARI) a(n) = {if (n == 1, return (0)); tau = (1 + sqrt(5))/2; mn = 0; while ((m = round(mn*tau)) < n, mn++; ); if (m == n, return (2*a(mn)+1)); mn = 0; while ((m = floor(mn*(1+tau)-tau/2)) < n, mn++; ); if (m == n, return (2*a(mn))); error("neither A nor B !!"); } \\ (cf C. Mongoven link) Michel Marcus, May 21 2013, Sep 02 2013
(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) = fromdigits(stol(n), 2); \\ Amiram Eldar, Jul 07 2023

Crossrefs

Cf. A048679, A200648, A200649, A200650, A200651.

Cf. A000120, A005811, A023416, A070939.

Sequence in context: A126314 A358139 A358654 * A086702 A156140 A324556

Adjacent sequences: A200711 A200712 A200713 * A200715 A200716 A200717

Keyword

nonn,base

Author

Casey Mongoven, Nov 20 2011

Extensions

More terms from Amiram Eldar, Jul 07 2023

Status

approved