A214970 - OEIS

%I #5 Oct 19 2012 13:49:30

%S 1,4,8,11,19,22,29,48,55,58,76,124,152,192,199,323,341,348,377,398,

%T 496,521,844,912,969,992,1042,1292,1364,2208,2255,2356,2388,2584,2728,

%U 3072,3376,3553,3571,5779,5952,6119,6169,6252,6752,6820,7142

%N 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.

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

%H Clark Kimberling, <a href="/A214970/b214970.txt">Table of n, a(n) for n = 1..50</a>

%e 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).

%t 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]]

%Y Cf. A214969, A214971.

%K nonn,base

%O 1,2

%A _Clark Kimberling_, Oct 17 2012