A372302 - OEIS

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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

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OFFSET

1,1

LINKS

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

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).

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).

Sequence in context: A046955 A042215 A041911 * A341327 A210288 A038125

Adjacent sequences: A372299 A372300 A372301 * A372303 A372304 A372305

KEYWORD

nonn

AUTHOR

A.H.M. Smeets, Apr 25 2024

STATUS

approved