A372302 - OEIS

%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