cp's OEIS Frontend

A364121 Stolarsky representation of n.

%I A364121 #10 Jul 07 2023 05:41:43
%S A364121 0,1,11,10,111,101,110,1111,100,1011,1101,1110,11111,1010,1001,10111,
%T A364121 1100,11011,11101,11110,111111,1000,10101,10011,10110,101111,11010,
%U A364121 11001,110111,11100,111011,111101,111110,1111111,10100,10001,101011,10010,100111,101101
%N A364121 Stolarsky representation of n.
%H A364121 Amiram Eldar, <a href="/A364121/b364121.txt">Table of n, a(n) for n = 1..10000</a>
%H A364121 Casey Mongoven, <a href="/A200648/a200648.txt">Description of Stolarsky Representations</a>.
%F A364121 Description of an algorithm for calculating a(n):
%F A364121 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 A364121 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 A364121 2. If n != round(round(n/phi)*phi) then s(n) = s(round(n/phi)) U {1}.
%F A364121 a(n) = A007088(A200714(n)).
%F A364121 A268643(a(n)) = A200649(n).
%F A364121 A055641(a(n)) = A200650(n).
%F A364121 A055642(a(n)) = A200648(n).
%F A364121 A043562(a(n)) = A200651(n)
%t A364121 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 A364121 a[n_] := FromDigits[stol[n]]; Array[a, 100]
%o A364121 (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 A364121 a(n) = fromdigits(stol(n));
%Y A364121 Cf. A001622, A007064, A200648, A200649, A200650, A200651, A200714.
%Y A364121 Cf. A007088, A043562, A055641, A055642, A268643.
%K A364121 nonn,base
%O A364121 1,3
%A A364121 _Amiram Eldar_, Jul 07 2023