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.

10, 15, 17, 57, 68, 520, 525, 547, 789, 894, 3149, 3700, 3845, 4272, 8304, 15792, 63555, 119926, 121267

Offset

1,1

Links

Table of n, a(n) for n=1..19.

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

Cf. A024816, A269307-A269312.

Sequence in context: A091049 A188579 A269985 * A139540 A343550 A285176

Adjacent sequences: A282645 A282646 A282647 * A282649 A282650 A282651

Keyword

nonn,base,more

Author

Paolo P. Lava, Feb 20 2017

Status

approved