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A187485

Positions of 0's in A123740; complement of A003623.

1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 25, 26, 27, 28, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 62, 64, 65, 67, 68, 69, 70, 72, 73, 74, 75, 77, 78, 80, 81, 82, 83, 85, 86, 88, 89, 90, 91, 93, 94, 95, 96, 98, 99, 101, 102, 103, 104, 106, 107, 108, 109, 111, 112, 114, 115, 116, 117, 119, 120

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OFFSET

1,2

COMMENTS

See A187950.

Positive integers k such that {k*phi} < {(k+2)*phi}, where phi = (1+sqrt(5))/2 and {...} denotes fractional part. - Jeffrey Shallit, Sep 23 2025

Shallit's condition can be simplified to {k*phi} < 1-{2*phi} = 4-2*phi. This shows that the asymptotic density of the sequence is 4-2*phi = 3-sqrt(5) = 0.763932... - Hans J. H. Tuenter, Feb 06 2026

LINKS

Hans J. H. Tuenter, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = floor(ceiling(n/2)*phi) + floor(n/2). - Hans J. H. Tuenter, Feb 06 2026

MATHEMATICA

r=(1+5^(1/2))/2;

seqA=Table[Floor[(n+4)r]-Floor[n*r]-6, {n, 1, 220}] (* A123740 *)

Flatten[Position[seqA, 0] ] (* A187485 *)

Flatten[Position[seqA, 1] ] (* A003623 *)

CROSSREFS

Cf. A187950, A123740.

Sequence in context: A084437 A037083 A188033 * A039052 A047572 A003233