A364122 Numbers whose Stolarsky representation (A364121) is palindromic.

1, 2, 3, 5, 6, 8, 13, 15, 18, 21, 23, 34, 36, 40, 45, 50, 55, 66, 71, 89, 91, 95, 108, 113, 120, 128, 136, 144, 159, 176, 196, 204, 233, 235, 239, 261, 273, 286, 291, 298, 319, 327, 338, 351, 364, 377, 400, 426, 464, 490, 518, 550, 563, 610, 612, 616, 654, 667

Offset: 1

Author

Amiram Eldar, Jul 07 2023

Keywords

• nonn
• base

Comments

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.

Fiboancci(2*n+1) + 2 is a term for n >= 3, since its Stolarsky representation is n-1 0's between two 1's.

Examples

			The first 10 terms are:
   n  a(n)  A364121(a(n))
  --  ----  -------------
   1     1  0
   2     2  1
   3     3  11
   4     5  111
   5     6  101
   6     8  1111
   7    13  11111
   8    15  1001
   9    18  11011
  10    21  111111
		

Links

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

Crossrefs

Cf. A000045, A200648, A200649, A200650, A200651, A200714, A364121.

Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087, A352105, A352319, A352341.

Programs

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}]]];
stolPalQ[n_]:= PalindromeQ[stol[n]]; Select[Range[700], stolPalQ]

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])));}
is(n) = {my(s = stol(n)); s == Vecrev(s);}