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A282648 Consider the antisigma function of a number x, A024816(x). Take the sum of its digits. Repeat the process deleting the first addendum and adding the previous sum. The sequence lists the numbers that after some iterations reach x.

%I A282648 #6 Feb 23 2017 22:53:30
%S A282648 10,15,17,57,68,520,525,547,789,894,3149,3700,3845,4272,8304,15792,
%T A282648 63555,119926,121267
%N A282648 Consider the antisigma function of a number x, A024816(x). Take the sum of its digits. Repeat the process deleting the first addendum and adding the previous sum. The sequence lists the numbers that after some iterations reach x.
%e A282648 68 * 69 / 2 - sigma(n) = 2220 and:
%e A282648 2 + 2 + 2 + 0 = 6;
%e A282648 2 + 2 + 0 + 6 = 10;
%e A282648 2 + 0 + 6 + 10 = 18;
%e A282648 0 + 6 + 10 + 18 = 34;
%e A282648 6 + 10 + 18 + 34 = 68.
%p A282648 with(numtheory): P:=proc(q, h) local a, b, k, n, t, v; v:=array(1..h);
%p A282648 for n from 2 to q do a:=n*(n+1)/2-sigma(n); b:=ilog10(a)+1; if b>1 then
%p A282648 for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
%p A282648 while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p A282648 if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000);
%Y A282648 Cf. A024816, A269307-A269312.
%K A282648 nonn,base,more
%O A282648 1,1
%A A282648 _Paolo P. Lava_, Feb 20 2017