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 A094202 Integers k whose Zeckendorf representation A014417(k) is palindromic. 30
 0, 1, 4, 6, 9, 12, 14, 22, 27, 33, 35, 51, 56, 64, 74, 80, 88, 90, 116, 127, 145, 158, 174, 184, 197, 203, 216, 232, 234, 276, 294, 326, 368, 378, 399, 425, 441, 462, 472, 493, 519, 525, 546, 572, 588, 609, 611, 679, 708, 760, 828, 847, 915, 944, 988, 1022, 1064, 1090 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES C. G. Lekkerkerker, Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci, Simon Stevin vol. 29, 1952, pages 190-195. E. Zeckendorf, Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas, Bulletin de la Société Royale des Sciences de Liège vol. 41 (1972) pages 179-182. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 129 terms from Indranil Ghosh) Ron Knott, Fibonacci Bases. EXAMPLE Fibonacci base columns are ...,8,5,3,2,1 with column entries 0 or 1 and no two consecutive ones (the Zeckendorf representation) so that each n has a unique representation. 12 is in the sequence because 12 = 8 + 3 + 1 = 10101 base Fib; 14 = 13 + 1 = 100001 base Fib. MATHEMATICA zeck[n_Integer] := Block[{k = Ceiling[ Log[ GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[ fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k-- ]; FromDigits[fr]]; a = {}; Do[z = zeck[n]; If[ FromDigits[ Reverse[ IntegerDigits[z]]] == z, AppendTo[a, n]], {n, 1123}]; a (* Robert G. Wilson v, May 29 2004 *) mirror[dig_, s_] := Join[dig, s, Reverse[dig]]; select[v_, mid_] := Select[v, Length[#] == 0 || Last[#] != mid &]; fib[dig_] := Plus @@ (dig * Fibonacci[Range[2, Length[dig] + 1]]); pals = Rest[IntegerDigits /@ FromDigits /@ Select[Tuples[{0, 1}, 7], SequenceCount[#, {1, 1}] == 0 &]]; Union@Join[{0, 1}, fib /@ Join[mirror[#, {}] & /@ (select[pals, 1]), mirror[#, {1}] & /@ (select[pals, 1]), mirror[#, {0}] & /@ pals]] (* Amiram Eldar, Jan 11 2020 *) PROG (Python) from sympy import fibonacci def a(n): k=0 x=0 while n>0: k=0 while fibonacci(k)<=n: k+=1 x+=10**(k - 3) n-=fibonacci(k - 1) return x def ok(n): x=str(a(n)) return x==x[::-1] print([n for n in range(1101) if ok(n)]) # Indranil Ghosh, Jun 07 2017 CROSSREFS Cf. A014417, A035517. Gives the positions of zeros in A095734. Subsets: A095730, A048757. A006995 gives the integers whose binary expansion is palindromic. Sequence in context: A122550 A191407 A076083 * A310666 A304231 A007074 Adjacent sequences: A094199 A094200 A094201 * A094203 A094204 A094205 KEYWORD nonn,base AUTHOR Ron Knott, May 25 2004 EXTENSIONS More terms from Robert G. Wilson v, May 28 2004 Offset changed to 1 by Alois P. Heinz, Aug 02 2017 STATUS approved

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Last modified October 2 14:37 EDT 2023. Contains 365837 sequences. (Running on oeis4.)