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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified October 18 17:13 EDT 2019. Contains 328186 sequences. (Running on oeis4.)