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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.
0
10, 15, 17, 57, 68, 520, 525, 547, 789, 894, 3149, 3700, 3845, 4272, 8304, 15792, 63555, 119926, 121267
OFFSET
1,1
EXAMPLE
68 * 69 / 2 - sigma(n) = 2220 and:
2 + 2 + 2 + 0 = 6;
2 + 2 + 0 + 6 = 10;
2 + 0 + 6 + 10 = 18;
0 + 6 + 10 + 18 = 34;
6 + 10 + 18 + 34 = 68.
MAPLE
with(numtheory): P:=proc(q, h) local a, b, k, n, t, v; v:=array(1..h);
for n from 2 to q do a:=n*(n+1)/2-sigma(n); b:=ilog10(a)+1; if b>1 then
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);
while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000);
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Paolo P. Lava, Feb 20 2017
STATUS
approved