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A269312
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Consider 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 the arithmetic derivative of x.
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7
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14, 51, 145, 285, 629, 708, 807, 1318, 2362, 2548, 2869, 3789, 4087, 4811, 6031, 6355, 10201, 15563, 17143, 17287, 17561, 19883, 20567, 21731, 22429, 23461, 26269, 27301, 30967, 33389, 69529, 73211, 85927, 86087, 90133, 96781, 110159, 116011, 159767, 161701, 162055, 190079
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OFFSET
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1,1
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LINKS
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Lars Blomberg, Table of n, a(n) for n = 1..663
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EXAMPLE
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14’ = 9 : 1 + 4 = 5; 4 + 5 = 9.
51’ = 20 : 5 + 1 = 6; 1 + 6 = 7; 6 + 7 = 13; 7 + 13 = 20.
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MAPLE
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with(numtheory): P:=proc(q, h) local a, b, c, k, n, p, t, v; v:=array(1..h);
for n from 1 to q do a:=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); c:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);
while v[t]<c do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=c then print(n); fi; fi; od; end: P(10^9, 1000);
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MATHEMATICA
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dn[n_] := If[Abs@n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@n]]]; (* after Michael Somos, Apr 12 2011 *)
Select[Range[10^5], # >= 10 && (s = dn[#]; d = IntegerDigits[#]; While[Total[d] < s, d = Join[Rest[d], {Total[d]}]]; Total[d] == s) &] (* Robert Price, May 22 2019 *)
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CROSSREFS
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Cf. A003415, A007629, A269307, A269308, A269309, A269310, A269311.
Sequence in context: A009961 A059997 A007588 * A129025 A113907 A125740
Adjacent sequences: A269309 A269310 A269311 * A269313 A269314 A269315
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KEYWORD
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nonn,base
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AUTHOR
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Paolo P. Lava, Feb 24 2016
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STATUS
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approved
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