%I #13 Feb 17 2018 14:00:32
%S 114,133,152,171,190,209,228,247,266,285,399
%N Numbers which are 19 times the sum of their digits.
%C The digit sums of the first 10 numbers are consecutive: 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. [Howard Berman (howard_berman(AT)hotmail.com), Apr 25 2009]
%C From _Bruno Berselli_, Nov 29 2013: (Start)
%C Numbers which are k times the sum of their digits:
%C k = 1: 1, 2, 3, 4, 5, 6, 7, 8, 9;
%C k = 2: 18;
%C k = 3: 27;
%C k = 4: 12, 24, 36, 48;
%C k = 5: 45;
%C k = 6: 54;
%C k = 7: 21, 42, 63, 84;
%C k = 8: 72;
%C k = 9: 81;
%C k = 10: 10, 20, 30, 40, 50, 60, 70, 80, 90;
%C k = 11: 198;
%C k = 12: 108;
%C k = 13: 117, 156, 195;
%C k = 14: 126;
%C k = 15: 135;
%C k = 16: 144, 192, 288;
%C k = 17: 153;
%C k = 18: 162;
%C k = 19: this sequence;
%C k = 20: 180;
%C k = 21: 378;
%C k = 22: 132, 264, 396;
%C k = 23: 207;
%C k = 24: 216;
%C k = 25: 150, 225, 375;
%C k = 26: 234, 468;
%C k = 27: 243, 486;
%C k = 28: 112, 140, 224, 252, 280, 308, 336, 364, 392, 448, 476, 588;
%C k = 29: 261;
%C k = 30: 270.
%C Also, k = 37 (prime) generates the list: 111, 222, 333, 370, 407, 444, 481, 518, 555, 592, 629, 666, 777, 888, 999. (End)
%e 114 = 19*(1+1+4), 133 = 19*(1+3+3) etc.
%t Select[Range[400],#==19*Total[IntegerDigits[#]]&] (* _Harvey P. Dale_, Feb 17 2018 *)
%Y Cf. A037478.
%K base,fini,full,nonn
%O 0,1
%A _Henry Bottomley_, Nov 20 2001