cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A331191 Numbers whose dual Zeckendorf representations (A104326) are palindromic.

This page as a plain text file.
%I A331191 #13 Sep 03 2022 05:39:18
%S A331191 0,1,3,4,6,11,12,16,19,22,32,33,38,42,48,53,64,71,87,88,98,106,110,
%T A331191 118,124,134,142,148,174,194,205,231,232,245,255,271,284,288,304,317,
%U A331191 323,336,346,362,375,402,420,462,474,516,548,566,608,609,635,656,666,687
%N A331191 Numbers whose dual Zeckendorf representations (A104326) are palindromic.
%C A331191 Pairs of numbers of the form {F(2*k-1)-2, F(2*k-1)-1}, for k >= 2, where F(k) is the k-th Fibonacci number, are consecutive terms in this sequence: {0, 1}, {3, 4}, {11, 12}, {32, 33}, ... - _Amiram Eldar_, Sep 03 2022
%H A331191 Amiram Eldar, <a href="/A331191/b331191.txt">Table of n, a(n) for n = 1..10000</a>
%e A331191 4 is a term since its dual Zeckendorf representation, 101, is palindromic.
%t A331191 mirror[dig_, s_] := Join[dig, s, Reverse[dig]];
%t A331191 select[v_, mid_] := Select[v, Length[#] == 0 || Last[#] != mid &];
%t A331191 fib[dig_] := Plus @@ (dig * Fibonacci[Range[2, Length[dig] + 1]]);
%t A331191 pals = Join[{{}}, Rest[Select[IntegerDigits[Range[0, 2^6 - 1], 2], SequenceCount[#, {0, 0}] == 0 &]]];
%t A331191 Union@Join[{0}, fib /@ Join[mirror[#, {}] & /@ (select[pals, 0]), mirror[#, {0}] & /@ (select[pals, 0]), mirror[#, {1}] & /@ pals]]
%Y A331191 Cf. A000045, A002113, A006995, A014190, A094202, A104326.
%K A331191 nonn,base
%O A331191 1,3
%A A331191 _Amiram Eldar_, Jan 11 2020