A095309 Numbers such that both their binary and Zeckendorf representations are palindromic.

0, 1, 3, 9, 27, 33, 51, 127, 1755, 2805, 10437, 71377, 547233, 1007727, 2924109, 3358515, 3460299, 59768775, 977921175, 1022225871, 1769996491, 5606742245, 13759209651, 15569747991, 120793923335, 426202820195, 6287935078637, 21296868044633, 25068131362413

Offset: 1

Author

Robert G. Wilson v, Jun 01 2004

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..38

Crossrefs

Intersection of A006995 and A094202.

Programs

Mathematica

fbz[n_] := Block[{k = Floor[ Log[ GoldenRatio, n*Sqrt[5]]], t = n, a = {}}, While[k > 1, If[Fibonacci[k] <= t, t = t - Fibonacci[k]; AppendTo[a, 1], AppendTo[a, 0]]; k-- ]; a]; Do[b = IntegerDigits[2n + 1, 2]; If[b == Reverse[b], f = fbz[2n + 1]; If[f == Reverse[f], Print[2n + 1]]], {n, 0, 10^9}]

Extensions

a(22)-a(29) from Chai Wah Wu, Jun 14 2018

a(1) = 0 added by Amiram Eldar, Jan 11 2020