A099143 Least k such that S(k) = S(k+n), or 0 if there is no k, where S is the Kempner function A002034.

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

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