A237994 a(n) is the smallest even k >= 2 such that the first n multiples of k have the same sum of digits, but (n + 1)*k has a different one. a(n) = 0 if no such k exists.

2, 126, 72, 486, 108, 54, 36, 2772, 0, 18, 918, 2376, 1782, 34650, 1728, 1584, 1386, 8910, 0, 1188, 95904, 6930, 87912, 479502, 81918, 75924, 73926, 792, 0, 71928, 65934, 63936, 67932, 14850, 61938, 594, 53946, 57942, 0, 51948, 1881198, 269730, 47952, 1148850

Offset

1,1

Links

Table of n, a(n) for n=1..44.

E. M. Langley, Problem 50. The sum of the digits of every multiple of 2739726 up to the 72nd is 36, The Mathematical Gazette, Vol. 1, No. 7 (April, 1896), pp. 20-21.

Example

a(72) = 2739726 since the sum of the digits of every multiple of 2739726 up to the 72nd is 36 while 2739726*73 = 199999998 has a different sum of digits.

Prog

(PARI) for(r=2, 45, n=0; if(Mod(r, 10)==0, print1(n, ", "), until(m==r, n=n+2; s=sumdigits(n); m=1; until(!(sumdigits(n*m)==s), m++)); print1(n, ", ")));

Crossrefs

Cf. A007953, A238088.

Sequence in context: A028481 A049659 A209602 * A348159 A157070 A064070

Adjacent sequences: A237991 A237992 A237993 * A237995 A237996 A237997

Keyword

nonn,base

Author

Arkadiusz Wesolowski, Feb 16 2014

Status

approved