A214970 Integers n that divide f(n), where f is the change-of-base function defined at A214969, using b = (golden ratio) and c=b^2.

1, 4, 8, 11, 19, 22, 29, 48, 55, 58, 76, 124, 152, 192, 199, 323, 341, 348, 377, 398, 496, 521, 844, 912, 969, 992, 1042, 1292, 1364, 2208, 2255, 2356, 2388, 2584, 2728, 3072, 3376, 3553, 3571, 5779, 5952, 6119, 6169, 6252, 6752, 6820, 7142

Offset

1,2

Comments

Conjecture: L(2k-1) and L(2k)+1 are terms of the sequence, for all positive integers k, where L=A000032 (Lucas numbers).

Links

Clark Kimberling, Table of n, a(n) for n = 1..50

Example

8 = r^4 + 1/r^4, where r = (1 + sqrt(5))/2 (the golden ratio), so f(8) = r^8 + 1/r^8 = 48, so 8 divides f(8).

Mathematica

r = GoldenRatio; f[x_] := Floor[Log[r, x]]; t[n_] := RealDigits[n, r, 1000]; p[n_] := Flatten[Position[t[n][[1]], 1]]; m[n_] := If[MemberQ[f[n] + 1 - p[n], 0], 1, 0]; t = Table[m[n], {n, 1, 900}]; Flatten[Position[t, 1]]

Crossrefs

Cf. A214969, A214971.

Sequence in context: A311075 A311076 A171070 * A233188 A220753 A166550

Adjacent sequences: A214967 A214968 A214969 * A214971 A214972 A214973

Keyword

nonn,base

Author

Clark Kimberling, Oct 17 2012

Status

approved