

A342726


Niven numbers in base i1: numbers that are divisible by the sum of their digits in base i1.


6



1, 2, 3, 4, 5, 6, 7, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 50, 54, 60, 64, 65, 66, 70, 77, 80, 88, 90, 96, 99, 100, 110, 112, 120, 124, 125, 126, 130, 140, 144, 145, 147, 150, 156, 160, 168, 170, 180, 182, 184, 185, 186, 190, 192
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OFFSET

1,2


COMMENTS

Numbers k that are divisible by A066323(k).
Equivalently, Niven numbers in base 4, since A066323(k) is also the sum of the digits of k in base 4.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Walter Penney, A "binary" system for complex numbers, Journal of the ACM, Vol. 12, No. 2 (1965), pp. 247248.


EXAMPLE

2 is a term since its representation in base i1 is 1100 and 1+1+0+0 = 2 is a divisor of 2.
10 is a term since its representation in base i1 is 111001100 and 1+1+1+0+0+1+1+0+0 = 5 is a divisor of 10.


MATHEMATICA

v = {{0, 0, 0, 0}, {0, 0, 0, 1}, {1, 1, 0, 0}, {1, 1, 0, 1}}; q[n_] := Divisible[n, Total[Flatten @ v[[1 + Reverse @ Most[Mod[NestWhileList[(#  Mod[#, 4])/4 &, n, # != 0 &], 4]]]]]]; Select[Range[200], q]


CROSSREFS

Cf. A007608, A066321, A066323, A271472, A342725, A342727, A342728, A342729.
Similar sequences: A005349 (decimal), A049445 (binary), A064150 (ternary), A064438 (quaternary), A064481 (base 5), A118363 (factorial), A328208 (Zeckendorf), A328212 (lazy Fibonacci), A331085 (negaFibonacci), A333426 (primorial), A334308 (base phi), A331728 (negabinary), A342426 (base 3/2).
Sequence in context: A072993 A018444 A032378 * A164947 A112881 A308019
Adjacent sequences: A342723 A342724 A342725 * A342727 A342728 A342729


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, Mar 19 2021


STATUS

approved



