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
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
KEYWORD
nonn,base,changed
AUTHOR
Casey Mongoven, Nov 20 2011
EXTENSIONS
More terms from Amiram Eldar, Jul 07 2023
STATUS
approved