A193772 Nonnegative integers whose digital difference is 0.

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 110, 202, 211, 220, 303, 312, 321, 330, 404, 413, 422, 431, 440, 505, 514, 523, 532, 541, 550, 606, 615, 624, 633, 642, 651, 660, 707, 716, 725, 734, 743, 752, 761, 770, 808, 817, 826, 835, 844, 853, 862, 871, 880

Offset: 1

Author

Dario Piazzalunga, Jan 02 2013

Keywords

• nonn
• base

Comments

The subsequence of multiples of 11 begins: 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 220, 330, 440...

The subsequence of primes begins: 11, 101, 211, 431, 523, 541, 743, 761, 853, ... (see A156307).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A040997, A007953, A156307.

Programs

Maple

V:= proc(n,s) # n-digits numbers with sum of digits s
     option remember; local i,k;
     `union`(seq(seq(map(t -> i*10^(n-1) + t, procname(k,s-i)),k=1..n-1),i=1..min(s,9)))
end proc:
for s from 0 to 9 do V(1,s) := {s} od:
f:= proc(n) local s,k;
   `union`(seq(seq(map(t -> s*10^(n-1) + t, V(k,s)), k=1..n-1),s=1..9))
end proc:
sort(convert(`union`(seq(f(d),d=1..4)),list)); # Robert Israel, Nov 14 2024

Mathematica

fQ[n_] := Module[{d = IntegerDigits[n]}, d[[1]] == Total[Rest[d]]]; Select[Range[0, 1000], fQ] (* T. D. Noe, Jan 02 2013 *)

Formula

If decimal expansion of n is x1 x2 ... xk then x1 - x2 - ... - xk = 0.

Extensions

Definition edited by Michel Marcus, Oct 26 2014