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A342726 Niven numbers in base i-1: numbers that are divisible by the sum of their digits in base i-1.

%I A342726 #10 Mar 21 2021 01:05:13
%S A342726 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,
%T A342726 50,54,60,64,65,66,70,77,80,88,90,96,99,100,110,112,120,124,125,126,
%U A342726 130,140,144,145,147,150,156,160,168,170,180,182,184,185,186,190,192
%N A342726 Niven numbers in base i-1: numbers that are divisible by the sum of their digits in base i-1.
%C A342726 Numbers k that are divisible by A066323(k).
%C A342726 Equivalently, Niven numbers in base -4, since A066323(k) is also the sum of the digits of k in base -4.
%H A342726 Amiram Eldar, <a href="/A342726/b342726.txt">Table of n, a(n) for n = 1..10000</a>
%H A342726 Walter Penney, <a href="http://dx.doi.org/10.1145/321264.321274">A "binary" system for complex numbers</a>, Journal of the ACM, Vol. 12, No. 2 (1965), pp. 247-248.
%e A342726 2 is a term since its representation in base i-1 is 1100 and 1+1+0+0 = 2 is a divisor of 2.
%e A342726 10 is a term since its representation in base i-1 is 111001100 and 1+1+1+0+0+1+1+0+0 = 5 is a divisor of 10.
%t A342726 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]
%Y A342726 Cf. A007608, A066321, A066323, A271472, A342725, A342727, A342728, A342729.
%Y A342726 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).
%K A342726 nonn,base
%O A342726 1,2
%A A342726 _Amiram Eldar_, Mar 19 2021