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A099143 Least k such that S(k) = S(k+n), or 0 if there is no k, where S is the Kempner function A002034. 1
0, 16, 3, 4, 5, 0, 7, 4, 9, 5, 11, 12, 13, 7, 5, 8, 17, 18, 19, 4, 7, 11, 23, 48, 5, 13, 9, 7, 16, 10, 31, 16, 11, 17, 5, 9, 37, 19, 9, 20, 41, 14, 43, 11, 15, 23, 47, 10192, 7, 10, 17, 13, 53, 18, 5, 7, 19, 29, 59, 60, 61, 18, 7, 16, 13, 11, 67, 17, 23, 14, 9, 18, 73, 16, 25, 19, 7, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The case of n=1 corresponds to the Tutescu conjecture, which states that the equation S(k) = S(k+1) has no solutions. It is conjectured that S(k) = S(k+6) also has no solutions. For odd prime p, a(p) = p. It appears that a(n) <= n, except for n = 1, 2, 6, 24, 48, 120, 240, 720 (A099144).

REFERENCES

L. Tutescu, "On a Conjecture Concerning the Smarandache Function." Abstracts of Papers Presented to the Amer. Math. Soc. 17, 583, 1996.

LINKS

Table of n, a(n) for n=1..78.

Eric Weisstein's World of Mathematics, Smarandache Function

MATHEMATICA

(*See A002034 for the Kempner function*) Table[i=1; While[i<10^5&&Kempner[i] != Kempner[i+n], i++ ]; If[i<10^5, i, 0], {n, 100}]

CROSSREFS

Cf. A099118 (number of times S(k+n) = S(k)), A099119 (greatest k such that S(k) = S(k-n)).

Sequence in context: A040248 A080992 A040249 * A070709 A247585 A068615

Adjacent sequences:  A099140 A099141 A099142 * A099144 A099145 A099146

KEYWORD

nonn

AUTHOR

T. D. Noe, Sep 30 2004

STATUS

approved

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Last modified March 26 01:08 EDT 2019. Contains 321479 sequences. (Running on oeis4.)