

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.


1



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
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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. 2021.


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 * A157070 A064070 A266993
Adjacent sequences: A237991 A237992 A237993 * A237995 A237996 A237997


KEYWORD

nonn,base


AUTHOR

Arkadiusz Wesolowski, Feb 16 2014


STATUS

approved



