A356395 - OEIS

%I #7 Aug 07 2022 07:52:33

%S 0,1,3,6,8,11,14,21,24,35,40,50,55,58,66,82,90,108,118,126,144,147,

%T 176,189,205,234,247,273,286,296,325,338,364,377,380,401,443,464,511,

%U 527,548,590,611,658,684,705,752,762,783,825,846,893,919,940,987,990

%N Nonnegative numbers k such that the negaFibonacci representation of k (A215022(k)) is palindromic.

%C See A094202 and A356396 for similar sequences.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/NegaFibonacci_coding">NegaFibonacci coding</a>

%H <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>

%e The first terms are:

%e   n   a(n)  A215022(a(n))

%e   --  ----  -------------

%e    1     0              0

%e    2     1              1

%e    3     3            101

%e    4     6          10001

%e    5     8          10101

%e    6    11        1001001

%e    7    14        1000001

%e    8    21        1010101

%e    9    24      100101001

%e   10    35      100000001

%o (PARI) is(n) = { my (v=0, neg=0, pos=0, f); for (e=0, oo, f=fibonacci(-1-e); if (f<0, neg+=f, pos+=f); if (neg <=n && n <= pos, while (n, if (f<0, neg-=f, pos-=f); if (neg > n || n > pos, v+=2^e; n-=f); f=fibonacci(-1-e--)); my (b=binary(v)); return (b==Vecrev(b)))) }

%Y Cf. A094202, A215022, A356396.

%K nonn,base

%O 1,3

%A _Rémy Sigrist_, Aug 05 2022