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Numbers k such that the sum of digits of 5k equals 10.
9

%I #18 Nov 29 2021 20:34:51

%S 11,29,38,47,56,65,74,83,92,101,110,128,146,164,182,209,218,227,236,

%T 245,254,263,272,281,290,308,326,344,362,380,407,416,425,434,443,452,

%U 461,470,488,506,524,542,560,605,614,623,632,641,650,668,686,704,722,740,803,812,821,830,848,866,884,902,920

%N Numbers k such that the sum of digits of 5k equals 10.

%C Inspired by A088407 = A069540/5 and A279769 (the analog for 9).

%H Michael S. Branicky, <a href="/A279775/b279775.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range@ 920, Total@ IntegerDigits[5 #] == 10 &] (* _Michael De Vlieger_, Dec 23 2016 *)

%o (PARI) select( is(n)=sumdigits(5*n)==10, [0..999])

%o (Python)

%o def ok(n): return sum(map(int, str(5*n))) == 10

%o print([k for k in range(921) if ok(k)]) # _Michael S. Branicky_, Nov 29 2021

%Y Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), 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,easy,base

%O 1,1

%A _M. F. Hasler_, Dec 23 2016