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

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

Offset

0,1

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)

Links

Table of n, a(n) for n=0..10.

Example

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

Mathematica

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

Crossrefs

Cf. A037478.

Sequence in context: A063991 A292020 A292019 * A219998 A095619 A160776

Adjacent sequences: A065115 A065116 A065117 * A065119 A065120 A065121

Keyword

base,fini,full,nonn

Author

Henry Bottomley, Nov 20 2001

Status

approved