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A094202 Integers n whose Zeckendorf representation A014417(n) is palindromic. 3
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

0,3

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, Representation 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

Table of n, a(n) for n=0..57.

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.

E.g., a(4) = 12 = 8 + 3 + 1 = 10101 base Fib; a(5) = 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 *)

CROSSREFS

Cf. 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 * A007074 A054087 A079255

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

STATUS

approved

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Last modified May 29 06:13 EDT 2015. Contains 257925 sequences.