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

1,2

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.

Links

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

Example

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

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]

Prog

(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); }

Crossrefs

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

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

Sequence in context: A087360 A111501 A094565 * A034722 A144712 A050028

Adjacent sequences: A364119 A364120 A364121 * A364123 A364124 A364125

Keyword

nonn,base

Author

Amiram Eldar, Jul 07 2023

Status

approved