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%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
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