

A334308


Base phi Niven numbers: numbers divisible by the number of 1's in their base phi representation (A055778).


8



1, 2, 6, 12, 15, 16, 18, 20, 30, 35, 36, 45, 48, 55, 60, 70, 72, 78, 84, 90, 91, 95, 96, 98, 104, 108, 132, 144, 147, 154, 168, 175, 184, 189, 208, 224, 231, 232, 245, 252, 256, 261, 264, 270, 275, 280, 282, 287, 294, 315, 322, 324, 330, 336, 340, 342, 351, 357
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OFFSET

1,2


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
F. Michel Dekking, The sum of digits function of the base phi expansion of the natural numbers, arXiv:1911.10705 [math.NT], 2019.
Ron Knott, Using Powers of Phi to represent Integers (Base Phi).
Wikipedia, Golden ratio base.


EXAMPLE

6 is a term since its base phi representation is 1010.0001, and the number of 1's is 3, which is a divisor of 6.


MATHEMATICA

phiDigSum[1] = 1; phiDigSum[n_] := Plus @@ RealDigits[n, GoldenRatio, 2*Ceiling[ Log[GoldenRatio, n]] ][[1]]; Select[Range[360], Divisible[#, phiDigSum[#]] &]


CROSSREFS

Cf. A005349, A049445, A055778, A064150, A064438, A064481, A118363, A328208, A328212, A333426.
Sequence in context: A152301 A152389 A114103 * A242336 A285312 A065154
Adjacent sequences: A334305 A334306 A334307 * A334309 A334310 A334311


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, Apr 22 2020


STATUS

approved



