%I #28 May 12 2024 11:18:21

%S 6,19,27,40,53,61,74,82,95,108,116,129,142,150,163,171,184,197,205,

%T 218,226,239,252,260,273,286,294,307,315,328,341,349,362,375,383,396,

%U 404,417,430,438,451,459,472,485,493,506,519,527,540,548,561,574,582,595,603

%N Numbers k for which the Zeckendorf representation A014417(k) ends with "1001".

%H A.H.M. Smeets, <a href="/A372302/b372302.txt">Table of n, a(n) for n = 1..20000</a>

%F Equals {A134859}\{A151915}.

%F a(n) = A134863(n) - 1 = A035338(n) + 1.

%F a(n) = a(n-1) + 8 + 5*A005614(n-2) = a(n-1) + F(6) + F(5)*A005614(n-2), n > 1, where F(k) is the k-th Fibonacci number (A000045).

%Y Cf. A000045, A005614, A014417.

%Y Tree of Zeckendorf subsequences of positive integers partitioned by their suffix part S (except initial term or offset in some cases). $ is the empty string. length(S) =

%Y 0 1 2 3 4 5 6 7

%Y ----------------------------------------------------------------------

%Y $: 0: 00: 000: 0000: 00000: 000000:

%Y A000027 A022342 A026274 A101345 A101642 notOEIS notOEIS

%Y 100000: 0100000:

%Y A035340 <------

%Y 10000:

%Y A035339

%Y 1000: 01000:

%Y A035338 <------

%Y 10: 010: 0010:

%Y A035336 <------ A134861

%Y 1010: 01010:

%Y A134863 <------

%Y 100: 0100:

%Y A035337 <------

%Y 1: 01: 001: 0001:

%Y A003622 <------ A134859 A151915

%Y 1001: 01001:

%Y A372302 <------

%Y 101: 0101:

%Y A134860 <------

%Y Suffixes 10^n, where ^ means n times repeated concatenation, are the (n+1)-th columns in the Wythoff array A083412 and A035513 (n >= 0).

%K nonn

%O 1,1

%A _A.H.M. Smeets_, Apr 25 2024