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Numbers k such that the sum of digits of 9k is 27.
10

%I #21 May 13 2022 18:15:54

%S 111,211,221,222,311,321,322,331,332,333,411,421,422,431,432,433,441,

%T 442,443,444,511,521,522,531,532,533,541,542,543,544,551,552,553,554,

%U 555,611,621,622,631,632,633,641,642,643,644,651,652,653,654,655,661

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

%C 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 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 Select[Range@ 661, Total@ IntegerDigits[9 #] == 27 &] (* _Michael De Vlieger_, Dec 23 2016 *)

%o (PARI) is(n)=sumdigits(9*n)==27

%Y Cf. A008591, A084854, A003991, A004247, A279769 (sumdigits(9n) = 18).

%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 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 Cf. A007953 (digital sum), A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).

%Y Cf. A082259.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Dec 23 2016