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A064438 Numbers which are divisible by the sum of their quaternary digits. 10
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, 21, 24, 28, 30, 32, 33, 35, 36, 40, 42, 48, 50, 52, 54, 60, 63, 64, 66, 68, 69, 72, 76, 78, 80, 81, 84, 88, 90, 91, 96, 100, 102, 108, 112, 114, 120, 126, 128, 129, 132, 136, 138, 140, 144, 148, 150, 154, 156, 160, 162, 168, 171, 180 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A good "puzzle" sequence -- guess the rule given the first twenty or so terms.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

Paul Dalenberg and Tom Edgar, Consecutive factorial base Niven numbers, Fibonacci Quart. (2018) Vol. 56, No. 2, 163-166.

EXAMPLE

Quaternary representation of 28 is 130, 1 + 3 + 0 = 4 divides 28.

MATHEMATICA

Select[Range[200], Divisible[#, Total[IntegerDigits[#, 4]]]&] (* Harvey P. Dale, Jun 09 2011 *)

PROG

(ARIBAS): maxarg := 190; for n := 1 to maxarg do if n mod sum(quaternarray(n)) = 0 then write(n, " "); end; end; function quaternarray(n: integer): array; var k: integer; stk: stack; begin while n > 0 do k := n mod 4; stack_push(stk, k); n := (n - k) div 4; end; return stack2array(stk); end; .

(PARI)

SumD(x)= { local(s); s=0; while (x>9, s+=x-10*(x\10); x\=10); return(s + x) }

baseE(x, b)= { local(d, e, f); e=0; f=1; while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) }

{ n=0; for (m=1, 10^9, if (m%(SumD(baseE(m, 4)))==0, write("b064438.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 14 2009

(PARI) isok(n) = !(n % sumdigits(n, 4)); \\ Michel Marcus, Jun 24 2018

(Python)

from sympy.ntheory.factor_ import digits

print([n for n in range(1, 201) if n%sum(digits(n, 4)[1:]) == 0]) # Indranil Ghosh, Apr 24 2017

CROSSREFS

Cf. A005349 (decimal), A049445 (binary), A064150 (ternary).

Sequence in context: A048716 A010434 A074230 * A227731 A067947 A279542

Adjacent sequences:  A064435 A064436 A064437 * A064439 A064440 A064441

KEYWORD

base,easy,nice,nonn,changed

AUTHOR

Len Smiley, Oct 01 2001

EXTENSIONS

More terms from Matthew Conroy, Oct 02 2001

Offset changed from 0 to 1 by Harry J. Smith, Sep 14 2009

STATUS

approved

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Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)