A279769 - OEIS

%I #29 Dec 23 2016 21:37:03

%S 11,21,22,31,32,33,41,42,43,44,51,52,53,54,55,61,62,63,64,65,66,71,72,

%T 73,74,75,76,77,81,82,83,84,85,86,87,88,91,92,93,94,95,96,97,98,99,

%U 101,102,103,104,105,106,107,108,109,110,121,122,131,132,133,141

%N Numbers n such that the sum of digits of 9n is 18.

%C Differs from A084854 from a(55) = 110 on.

%C Numbers n such that A008591(n) is a term of A235228. - _Felix Fröhlich_, Dec 18 2016

%C The digital sum of 9n is always a multiple of 9, and never zero. For most numbers < 100, the digital sum is equal to 9, but for example in the range [91..110] all numbers except 100 have their digital sum equal to 18. The b-file / graph gives a hint on the "asymptotic" distribution / density of this set. After a "flat" range like that at [91..110] there comes a record gap. Sizes [and upper ends] of record gaps are: 10 [a(2) = 21], 11 [a(56) = 121, a(119) = 231, a(188) = 341, ..., a(553) = 891, a(616) = 1001], 21 [a(671) = 1121], 31 [a(1331) = 2231], ..., 91 [a(4339) = 8891], 101 [a(4621) = 10001], 121 [a(4841) = 11121], 231 [a(9176) = 22231], ..., 891 [a(24217) = 88891], 1001 [a(25213) = 100001], 1121 [a(25928) = 111121], 2231 [a(47510) = 222231], ..., 8891 [a(108577) = 888891], 10001 [a(111574) = 1000001], 11121 [a(113576) = 1111121], 22231 [a(202511) = 2222231], ..., 88891 [a(416215) = 8888891], ... - _M. F. Hasler_, Dec 22 2016

%H M. F. Hasler, <a href="/A279769/b279769.txt">Table of n, a(n) for n = 1..25212</a>

%F a(n) = A235228(n)/9.

%t Select[Range@ 141, Total@ IntegerDigits[9 #] == 18 &]

%o (PARI) is(n) = sumdigits(9*n)==18 \\ _Felix Fröhlich_, Dec 18 2016

%Y Cf. A007953 (digital sum), A008591, A084854.

%Y Cf. A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).

%Y Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.

%Y Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).

%Y Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Dec 18 2016