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Numbers which are 19 times the sum of their digits.
0

%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