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A064438 Numbers which are divisible by the sum of their quaternary digits. 4
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, 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 xrange(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

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 June 18 14:52 EDT 2019. Contains 324213 sequences. (Running on oeis4.)