A346211 Numbers m such that abs(K(m+1) - K(m)) = 1, where K(m) = A002034(m) is the Kempner function.

1, 2, 3, 4, 9, 15, 35, 63, 99, 175, 195, 483, 1443, 2057, 2115, 2299, 3363, 3843, 5082, 5475, 6723, 7865, 11235, 11913, 12005, 22747, 24963, 26978, 27555, 31683, 37635, 41514, 46255, 51075, 62464, 68643, 76704, 77283, 89375, 95874, 98595, 104975, 105412, 113398

Offset

1,2

Comments

Florentin Smarandache (Muller, 1990) and Tutescu (1996) conjectured that there is no number m such that K(m) = K(m+1), and Weisstein (2004) verified it up to m = 10^9.

a(1)-a(40) were calculated by Earls (2005).

References

Lucian Tutescu, On a Conjecture Concerning the Smarandache Function, Abstracts of Papers Presented to the Amer. Math. Soc., Vol. 17 (1996), p. 583.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Jason Earls, On consecutive values of the Smarandache function, Scientia Magna, Vol. 1, No. 1 (2005), pp. 129-130.

R. Muller, Smarandache Function Journal, Vol. 1 (1990), p. 37.

Eric Weisstein's World of Mathematics, Smarandache Function.

Wikipedia, Kempner function.

Example

1 is a term since K(2) - K(1) = 2 - 1 = 1.

Mathematica

kempner[n_] := Module[{m = 1}, While[! Divisible[m!, n], m++]; m]; Position[Abs @ Differences @ Array[kempner, 500], 1] // Flatten

Crossrefs

Cf. A002034, A346212.

Sequence in context: A248647 A284437 A049909 * A096781 A232055 A192818

Adjacent sequences: A346208 A346209 A346210 * A346212 A346213 A346214

Keyword

nonn

Author

Amiram Eldar, Jul 10 2021

Status

approved