A364121 - OEIS

%I #10 Jul 07 2023 05:41:43

%S 0,1,11,10,111,101,110,1111,100,1011,1101,1110,11111,1010,1001,10111,

%T 1100,11011,11101,11110,111111,1000,10101,10011,10110,101111,11010,

%U 11001,110111,11100,111011,111101,111110,1111111,10100,10001,101011,10010,100111,101101

%N Stolarsky representation of n.

%H Amiram Eldar, <a href="/A364121/b364121.txt">Table of n, a(n) for n = 1..10000</a>

%H Casey Mongoven, <a href="/A200648/a200648.txt">Description of Stolarsky Representations</a>.

%F Description of an algorithm for calculating a(n):

%F Let s(1) = {} be the empty set, and for n > 1, let s(n) be the sequence of digits of a(n). s(n) can be calculated recursively by:

%F 1. If n = round(round(n/phi)*phi) then s(n) = s(floor(n/phi^2) + 1) U {0}, where phi is the golden ratio (A001622) and U denotes concatenation.

%F 2. If n != round(round(n/phi)*phi) then s(n) = s(round(n/phi)) U {1}.

%F a(n) = A007088(A200714(n)).

%F A268643(a(n)) = A200649(n).

%F A055641(a(n)) = A200650(n).

%F A055642(a(n)) = A200648(n).

%F A043562(a(n)) = A200651(n)

%t 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}]]];

%t a[n_] := FromDigits[stol[n]]; Array[a, 100]

%o (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])));}

%o a(n) = fromdigits(stol(n));

%Y Cf. A001622, A007064, A200648, A200649, A200650, A200651, A200714.

%Y Cf. A007088, A043562, A055641, A055642, A268643.

%K nonn,base

%O 1,3

%A _Amiram Eldar_, Jul 07 2023