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A255354
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a(n) = smallest number k such that (k + n)' = k', or -1 if no such number exists, where k' is the arithmetic derivative of k.
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0
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2, 3, 2, 3, 2, 5, 110, 3, 2, 3, 2, 5, 50145, 3, 2, 3, 2, 5, 53115, 3, 2, 7, 189, 5, 273, 3, 2, 3, 2, 7, 75, 5, 930642191642, 3, 2, 5, 165, 3, 2, 3, 2, 5, 12, 3, 2, 7, 99, 5, 182, 3, 2, 7, 706, 5, 1523965807, 3, 2, 3, 2, 7, 494, 5
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OFFSET
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1,1
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COMMENTS
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The sequence begins (first 100 terms):
2, 3, 2, 3, 2, 5, 110, 3, 2, 3, 2, 5, 50145, 3, 2, 3, 2, 5, 53115, 3, 2, 7, 189, 5, 273, 3, 2, 3, 2, 7, 75, 5, 930642191642, 3, 2, 5, 165, 3, 2, 3, 2, 5, 12, 3, 2, 7, 99, 5, 182, 3, 2, 7, 706, 5, 1523965807, 3, 2, 3, 2, 7, 494, 5, -1, 3, 2, 5, 1151559, 3, 2, 3, 2, 7, 705, 5, 20, 3, 2, 5, 4526, 3, 2, 7, 1102, 5, 1509626, 3, 2, 13, 778, 7, 226429394, 5, -1, 3, 2, 5, 1910, 3, 2, 3 where the other missing terms (designated by -1: a(63), a(93)) are > 10^12, if they exist).
a(91) = 226429394. - Michel Marcus, Feb 28 2015
a(63), a(93) > 10^12. - Giovanni Resta, Jun 22 2018
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LINKS
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Table of n, a(n) for n=1..62.
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EXAMPLE
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a(1) = 2 because (2 + 1)' = 2' = 1.
a(2) = 3 because (3 + 2)' = 3' = 1.
a(3) = 2 because (2 + 3)' = 2' = 1.
...
a(7) = 110 because (110 + 7)' = 110' = . Etc.
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MAPLE
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with(numtheory): P:=proc(q) local a, b, k, n, p;
for n from 1 to q do for k from 1 to q do
a:=k*add(op(2, p)/op(1, p), p=ifactors(k)[2]); b:=(k+n)*add(op(2, p)/op(1, p), p=ifactors(k+n)[2]);
if a=b then print(k); break; fi; od;
od; end: P(10^20);
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CROSSREFS
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Cf. A003415, A007015, A007365, A015886, A065559.
Sequence in context: A087317 A086489 A015886 * A344349 A318620 A287748
Adjacent sequences: A255351 A255352 A255353 * A255355 A255356 A255357
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KEYWORD
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nonn,more
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AUTHOR
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Paolo P. Lava, Feb 24 2015
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EXTENSIONS
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a(33)-a(62) from Giovanni Resta, Jun 22 2018
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STATUS
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approved
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