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.

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, 65, 33, 67, 34, 69

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

Mathematica

s[n_, b_] := Module[{m, t}, t = 0; m = n; While[m != 0 , t = t + Mod[m, b]; m = Quotient[m, b]]; t];
a[n_] := Module[{m}, For[m = 1, Mod[s[m*(n-1), 2], 2] != 0 || Mod[s[2*m*(n-1), n]/(n-1), 2] != 0, m++]; m];
Table[a[n], {n, 2, 100}](* Jean-François Alcover, May 20 2025, after Alois P. Heinz *)

Crossrefs

Cf. A026741, A145051.

Sequence in context: A249304 A333906 A306224 * A153098 A388826 A329509

Adjacent sequences: A189199 A189200 A189201 * A189203 A189204 A189205

Keyword

nonn

Author

Vladimir Shevelev, May 02 2011

Status

approved