A334308 Base phi Niven numbers: numbers divisible by the number of 1's in their base phi representation (A055778).

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

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