cp's OEIS Frontend

A279777 Numbers k such that the sum of digits of 9k is 27.

%I A279777 #21 May 13 2022 18:15:54
%S A279777 111,211,221,222,311,321,322,331,332,333,411,421,422,431,432,433,441,
%T A279777 442,443,444,511,521,522,531,532,533,541,542,543,544,551,552,553,554,
%U A279777 555,611,621,622,631,632,633,641,642,643,644,651,652,653,654,655,661
%N A279777 Numbers k such that the sum of digits of 9k is 27.
%C A279777 The digital sum of 9k is always a multiple of 9. For most numbers below 100 it is actually equal to 9. Numbers such that the digital sum of 9k is 18 are listed in A279769. Only every third term of the present sequence is divisible by 3.
%C A279777 The sequence of record gaps [and upper end of the gap] is: 100 [a(2) = 211], 101 [a(221) = 1211], 111 [a(4841) = 11211], 111 [a(10121) = 22311], 111 [a(15752) = 33411], ..., 111 [a(45133) = 88911], 111 [a(50413) = 100011], 211 [a(55253) = 111211], 311 [a(110000) = 222311], ..., 911 [a(380557) = 888911], 1011 [a(411049) = 1000011], 1211 [a(436976) = 1111211], 2311 [a(840281) = 2222311], ..., 8911 [a(2451241) = 8888911], ...
%t A279777 Select[Range@ 661, Total@ IntegerDigits[9 #] == 27 &] (* _Michael De Vlieger_, Dec 23 2016 *)
%o A279777 (PARI) is(n)=sumdigits(9*n)==27
%Y A279777 Cf. A008591, A084854, A003991, A004247, A279769 (sumdigits(9n) = 18).
%Y A279777 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 A279777 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).
%Y A279777 Cf. A007953 (digital sum), A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
%Y A279777 Cf. A082259.
%K A279777 nonn,base
%O A279777 1,1
%A A279777 _M. F. Hasler_, Dec 23 2016