A065118 Numbers which are 19 times the sum of their digits.

114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 399

Offset: 0

Author

Henry Bottomley, Nov 20 2001

Keywords

• base
• fini
• full
• nonn

Comments

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]

From Bruno Berselli, Nov 29 2013: (Start)

Numbers which are k times the sum of their digits:

k = 1: 1, 2, 3, 4, 5, 6, 7, 8, 9;

k = 2: 18;

k = 3: 27;

k = 4: 12, 24, 36, 48;

k = 5: 45;

k = 6: 54;

k = 7: 21, 42, 63, 84;

k = 8: 72;

k = 9: 81;

k = 10: 10, 20, 30, 40, 50, 60, 70, 80, 90;

k = 11: 198;

k = 12: 108;

k = 13: 117, 156, 195;

k = 14: 126;

k = 15: 135;

k = 16: 144, 192, 288;

k = 17: 153;

k = 18: 162;

k = 19: this sequence;

k = 20: 180;

k = 21: 378;

k = 22: 132, 264, 396;

k = 23: 207;

k = 24: 216;

k = 25: 150, 225, 375;

k = 26: 234, 468;

k = 27: 243, 486;

k = 28: 112, 140, 224, 252, 280, 308, 336, 364, 392, 448, 476, 588;

k = 29: 261;

k = 30: 270.

Also, k = 37 (prime) generates the list: 111, 222, 333, 370, 407, 444, 481, 518, 555, 592, 629, 666, 777, 888, 999. (End)

Examples

			114 = 19*(1+1+4), 133 = 19*(1+3+3) etc.
		

Crossrefs

Cf. A037478.

Programs

Mathematica

Select[Range[400],#==19*Total[IntegerDigits[#]]&] (* Harvey P. Dale, Feb 17 2018 *)