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A189202 Let s_k(n) denote the sum of digits of n in base k. Then a(n) is the smallest m>0 such that both s_2(m*(n-1)) and s_n(2*m*(n-1))/(n-1) are even, or a(n)=0, if such m does not exist. 1
3, 5, 5, 3, 13, 4, 9, 5, 11, 6, 19, 20, 15, 47, 17, 9, 19, 10, 21, 32, 23, 12, 37, 13, 40, 41, 29, 15, 46, 16, 33, 17, 35, 18, 37, 56, 39, 20, 41, 21, 85, 22, 45, 68, 47, 72, 73, 25, 51, 26, 79, 80, 109, 28, 57, 87, 59, 30, 91, 153, 63, 191 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Conjecture: For all n>=2, a(n)>0.

For a general problem, see SeqFan link.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..10000

Vladimir Shevelev, "A new digital problem", SeqFan Discussion, Apr 2011.

MAPLE

s:= proc(n, b) local m, t;

      t:= 0; m:= n;

      while m<>0 do t:= t+ irem(m, b, 'm') od; t

    end:

a:= proc(n) local m;

      for m while irem(s(m*(n-1), 2), 2)<>0 or

                  irem(s(2*m*(n-1), n)/(n-1), 2)<>0 do od; m

    end:

seq(a(n), n=2..100);  # Alois P. Heinz, May 02 2011

CROSSREFS

Cf. A026741, A145051.

Sequence in context: A328154 A249304 A306224 * A153098 A119280 A307634

Adjacent sequences:  A189199 A189200 A189201 * A189203 A189204 A189205

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 02 2011

STATUS

approved

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Last modified October 14 09:57 EDT 2019. Contains 327995 sequences. (Running on oeis4.)