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A193772 Nonnegative integers whose digital difference is 0.

%I A193772 #36 Nov 15 2024 13:25:45
%S A193772 0,11,22,33,44,55,66,77,88,99,101,110,202,211,220,303,312,321,330,404,
%T A193772 413,422,431,440,505,514,523,532,541,550,606,615,624,633,642,651,660,
%U A193772 707,716,725,734,743,752,761,770,808,817,826,835,844,853,862,871,880
%N A193772 Nonnegative integers whose digital difference is 0.
%C A193772 The subsequence of multiples of 11 begins: 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 220, 330, 440...
%C A193772 The subsequence of primes begins: 11, 101, 211, 431, 523, 541, 743, 761, 853, ... (see A156307).
%H A193772 Robert Israel, <a href="/A193772/b193772.txt">Table of n, a(n) for n = 1..10000</a>
%F A193772 If decimal expansion of n is x1 x2 ... xk then x1 - x2 - ... - xk = 0.
%p A193772 V:= proc(n,s) # n-digits numbers with sum of digits s
%p A193772      option remember; local i,k;
%p A193772      `union`(seq(seq(map(t -> i*10^(n-1) + t, procname(k,s-i)),k=1..n-1),i=1..min(s,9)))
%p A193772 end proc:
%p A193772 for s from 0 to 9 do V(1,s) := {s} od:
%p A193772 f:= proc(n) local s,k;
%p A193772    `union`(seq(seq(map(t -> s*10^(n-1) + t, V(k,s)), k=1..n-1),s=1..9))
%p A193772 end proc:
%p A193772 sort(convert(`union`(seq(f(d),d=1..4)),list)); # _Robert Israel_, Nov 14 2024
%t A193772 fQ[n_] := Module[{d = IntegerDigits[n]}, d[[1]] == Total[Rest[d]]]; Select[Range[0, 1000], fQ] (* _T. D. Noe_, Jan 02 2013 *)
%Y A193772 Cf. A040997, A007953, A156307.
%K A193772 nonn,base
%O A193772 1,2
%A A193772 _Dario Piazzalunga_, Jan 02 2013
%E A193772 Definition edited by _Michel Marcus_, Oct 26 2014