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A364122 Numbers whose Stolarsky representation (A364121) is palindromic.

%I A364122 #8 Jul 07 2023 05:41:57
%S A364122 1,2,3,5,6,8,13,15,18,21,23,34,36,40,45,50,55,66,71,89,91,95,108,113,
%T A364122 120,128,136,144,159,176,196,204,233,235,239,261,273,286,291,298,319,
%U A364122 327,338,351,364,377,400,426,464,490,518,550,563,610,612,616,654,667
%N A364122 Numbers whose Stolarsky representation (A364121) is palindromic.
%C A364122 The positive Fibonacci numbers (A000045) are terms since the Stolarsky representation of Fibonacci(1) = Fibonacci(2) is 0 and the Stolarsky representation of Fibonacci(n) is n-2 1's for n >= 3.
%C A364122 Fiboancci(2*n+1) + 2 is a term for n >= 3, since its Stolarsky representation is n-1 0's between two 1's.
%H A364122 Amiram Eldar, <a href="/A364122/b364122.txt">Table of n, a(n) for n = 1..10000</a>
%e A364122 The first 10 terms are:
%e A364122    n  a(n)  A364121(a(n))
%e A364122   --  ----  -------------
%e A364122    1     1  0
%e A364122    2     2  1
%e A364122    3     3  11
%e A364122    4     5  111
%e A364122    5     6  101
%e A364122    6     8  1111
%e A364122    7    13  11111
%e A364122    8    15  1001
%e A364122    9    18  11011
%e A364122   10    21  111111
%t A364122 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 A364122 stolPalQ[n_]:= PalindromeQ[stol[n]]; Select[Range[700], stolPalQ]
%o A364122 (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 A364122 is(n) = {my(s = stol(n)); s == Vecrev(s);}
%Y A364122 Cf. A000045, A200648, A200649, A200650, A200651, A200714, A364121.
%Y A364122 Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087, A352105, A352319, A352341.
%K A364122 nonn,base
%O A364122 1,2
%A A364122 _Amiram Eldar_, Jul 07 2023