A131418 Numbers n such that Sum_digits(n)=Sum_digits[n+Sum_digits(n)], with n>=0.

0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 108, 117, 126, 135, 144, 153, 162, 171, 207, 216, 225, 234, 243, 252, 261, 279, 306, 315, 324, 333, 342, 351, 369, 378, 405, 414, 423, 432, 441, 459, 468, 477, 504, 513, 522, 531, 549, 558, 567, 576, 603, 612, 621, 639

Offset

1,2

Comments

Conjecture: all terms are divisible by 9. - Harvey P. Dale, Mar 28 2019

Links

Table of n, a(n) for n=1..54.

Example

n=315 --> 3+1+5=9 --> 315+9=324 --> 3+2+4=9.
n=873 --> 8+7+3=18 --> 873+18=891 --> 8+9+1=18.

Maple

P:=proc(n) local a, i, k, w; for i from 0 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; a:=w; k:=i+w; w:=0; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if a=w then print(i); fi; od; end: P(1000);

Mathematica

Select[Range[0, 700], Total[IntegerDigits[#]]==Total[IntegerDigits[#+ Total[ IntegerDigits[ #]]]]&] (* Harvey P. Dale, Mar 28 2019 *)

Prog

(PARI) isok(n) = my(sn = sumdigits(n)); sn == sumdigits(n+sn); \\ Michel Marcus, May 10 2019

Crossrefs

Cf. A007953, A131417.

Sequence in context: A111708 A248050 A044052 * A249605 A130692 A043453

Adjacent sequences: A131415 A131416 A131417 * A131419 A131420 A131421

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 09 2007

Status

approved