A372302 Numbers k for which the Zeckendorf representation A014417(k) ends with "1001".

6, 19, 27, 40, 53, 61, 74, 82, 95, 108, 116, 129, 142, 150, 163, 171, 184, 197, 205, 218, 226, 239, 252, 260, 273, 286, 294, 307, 315, 328, 341, 349, 362, 375, 383, 396, 404, 417, 430, 438, 451, 459, 472, 485, 493, 506, 519, 527, 540, 548, 561, 574, 582, 595, 603

Offset: 1

Author

A.H.M. Smeets, Apr 25 2024

Keywords

• nonn

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000045, A005614, A014417.

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) =

0 1 2 3 4 5 6 7

----------------------------------------------------------------------

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

A000027 A022342 A026274 A101345 A101642 notOEIS notOEIS

100000: 0100000:

A035340 <------

10000:

A035339

1000: 01000:

A035338 <------

10: 010: 0010:

A035336 <------ A134861

1010: 01010:

A134863 <------

100: 0100:

A035337 <------

1: 01: 001: 0001:

A003622 <------ A134859 A151915

1001: 01001:

A372302 <------

101: 0101:

A134860 <------

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

Formula

Equals {A134859}\{A151915}.

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

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).