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A364122
Numbers whose Stolarsky representation (A364121) is palindromic.
1
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
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); }
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jul 07 2023
STATUS
approved