The On-Line Encyclopedia of Integer Sequences (OEIS)

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A269311 revision #10

A269311

Consider the arithmetic derivative of a number 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.

8, 18, 21, 160, 1590, 2420, 18620, 69229, 83790, 279964, 494520, 598810, 676450, 1183147, 4233720, 5600348, 14217074, 20025836, 64278677, 425208387, 604048830, 750851470, 1981942354

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

8’ = 12 : 1 + 2 = 3; 2 + 3 = 5; 3 + 5 = 8.

18’ = 21 : 2 + 1 = 3; 1 + 3 = 4; 3 + 4 = 7; 4 + 7 = 11; 7 + 11 = 18.

MAPLE

with(numtheory): P:=proc(q, h) local a, b, k, p, t, v; global n; v:=array(1..h);

for n from 1 to q do a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]); 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);