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A173443 Minimal positive integer such that the smallest possible sum of digits of its multiple equals n. 0
1, 7, 3, 79, 41, 33, 239, 2629, 9, 2981, 21649, 813, 3000811, 51139, 13947, 5165039 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= (10^n-1)/9. a(3n) <= (10^n-1)/3.

Many, but not all of a(n) are the divisors of (10^n-1)/9.

a(17)<=5363222357, a(18)=99, a(20)=12344321, a(21)=243309, a(24)<=33333333, a(27)=999

LINKS

Table of n, a(n) for n=1..16.

Author?, On sum of digits and one open problem (in Russian)

Author?, Discussion on scientific forum dxdy.ru (in Russian)

FORMULA

a(n) = smallest m such that A077196(m)=n.

a(9n) = 10^n - 1.

EXAMPLE

a(4)=79 because the sum of digits of 79*1519=120001 is 4; there is no multiple of 79 whose sum of digits is less than 4; and there is no integer smaller than 79, for which the minimal sum of digits in its multiple is 4.

CROSSREFS

Cf. A077194, A077195, A077196.

Sequence in context: A176328 A248279 A183421 * A003723 A241438 A054471

Adjacent sequences:  A173440 A173441 A173442 * A173444 A173445 A173446

KEYWORD

base,hard,more,nonn

AUTHOR

Alexey Izvalov, Feb 18 2010

EXTENSIONS

Edited by Max Alekseyev, Feb 19 2010, Nov 13 2010

a(21) and new bounds for a(13), a(16), a(17), a(20), a(24) from Max Alekseyev, Nov 14 2010

a(13), a(16), and a(20) from Max Alekseyev, Nov 17 2010, Nov 19 2010

STATUS

approved

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Last modified August 25 05:19 EDT 2019. Contains 326318 sequences. (Running on oeis4.)