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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
OFFSET
1,1
LINKS
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
Sequence in context: A028481 A049659 A209602 * A348159 A157070 A064070
KEYWORD
nonn,base
AUTHOR
STATUS
approved