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 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. 6
 8, 18, 21, 160, 1590, 2420, 18620, 69229, 83790, 279964, 494520, 598810, 676450, 1183147, 4233720, 5600348, 14217074, 20025836, 64278677, 425208387, 604048830, 750851470, 1981942354 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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); while v[t]= 10 && (d = IntegerDigits[dn[#]]; While[Total[d] < #, d = Join[Rest[d], {Total[d]}]]; Total[d] == #) &] (* Robert Price, May 22 2019 *) CROSSREFS Cf. A003415, A007629, A269307, A269308, A269309, A269310, A269312. Sequence in context: A108060 A279688 A178180 * A242185 A273527 A051810 Adjacent sequences:  A269308 A269309 A269310 * A269312 A269313 A269314 KEYWORD nonn,base,more AUTHOR Paolo P. Lava, Feb 24 2016 EXTENSIONS a(19)-a(23) from Lars Blomberg, Jan 18 2018 STATUS approved

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Last modified November 28 16:42 EST 2021. Contains 349413 sequences. (Running on oeis4.)