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A255354 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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

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.

MAPLE

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);

CROSSREFS

Cf. A003415, A007015, A007365, A015886, A065559.

Sequence in context: A087317 A086489 A015886 * A344349 A318620 A287748

Adjacent sequences:  A255351 A255352 A255353 * A255355 A255356 A255357

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Feb 24 2015

EXTENSIONS

a(33)-a(62) from Giovanni Resta, Jun 22 2018

STATUS

approved

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Last modified May 25 03:39 EDT 2022. Contains 354047 sequences. (Running on oeis4.)