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

1,2

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

Formula

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

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 *)

Crossrefs

Cf. A040997, A007953, A156307.

Sequence in context: A064544 A083967 A343444 * A178359 A108203 A308104

Adjacent sequences: A193769 A193770 A193771 * A193773 A193774 A193775

Keyword

nonn,base

Author

Dario Piazzalunga, Jan 02 2013

Extensions

Definition edited by Michel Marcus, Oct 26 2014

Status

approved