This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279769 #29 Dec 23 2016 21:37:03 %S A279769 11,21,22,31,32,33,41,42,43,44,51,52,53,54,55,61,62,63,64,65,66,71,72, %T A279769 73,74,75,76,77,81,82,83,84,85,86,87,88,91,92,93,94,95,96,97,98,99, %U A279769 101,102,103,104,105,106,107,108,109,110,121,122,131,132,133,141 %N A279769 Numbers n such that the sum of digits of 9n is 18. %C A279769 Differs from A084854 from a(55) = 110 on. %C A279769 Numbers n such that A008591(n) is a term of A235228. - _Felix Fröhlich_, Dec 18 2016 %C A279769 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 A279769 M. F. Hasler, <a href="/A279769/b279769.txt">Table of n, a(n) for n = 1..25212</a> %F A279769 a(n) = A235228(n)/9. %t A279769 Select[Range@ 141, Total@ IntegerDigits[9 #] == 18 &] %o A279769 (PARI) is(n) = sumdigits(9*n)==18 \\ _Felix Fröhlich_, Dec 18 2016 %Y A279769 Cf. A007953 (digital sum), A008591, A084854. %Y A279769 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 A279769 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 A279769 Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums). %Y A279769 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 A279769 nonn,base %O A279769 1,1 %A A279769 _M. F. Hasler_, Dec 18 2016