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%I #11 Jul 23 2021 05:30:53
%S 1,2,3,4,9,15,35,63,99,175,195,483,1443,2057,2115,2299,3363,3843,5082,
%T 5475,6723,7865,11235,11913,12005,22747,24963,26978,27555,31683,37635,
%U 41514,46255,51075,62464,68643,76704,77283,89375,95874,98595,104975,105412,113398
%N Numbers m such that abs(K(m+1) - K(m)) = 1, where K(m) = A002034(m) is the Kempner function.
%C 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.
%C a(1)-a(40) were calculated by Earls (2005).
%D Lucian Tutescu, On a Conjecture Concerning the Smarandache Function, Abstracts of Papers Presented to the Amer. Math. Soc., Vol. 17 (1996), p. 583.
%H Amiram Eldar, <a href="/A346211/b346211.txt">Table of n, a(n) for n = 1..1000</a>
%H Jason Earls, <a href="https://www.proquest.com/openview/0c5bbea3d77fcffda894d8c9397f592e">On consecutive values of the Smarandache function</a>, Scientia Magna, Vol. 1, No. 1 (2005), pp. 129-130.
%H R. Muller, <a href="https://doi.org/10.5281/zenodo.8934">Smarandache Function Journal</a>, Vol. 1 (1990), p. 37.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmarandacheFunction.html">Smarandache Function</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kempner_function">Kempner function</a>.
%e 1 is a term since K(2) - K(1) = 2 - 1 = 1.
%t kempner[n_] := Module[{m = 1}, While[! Divisible[m!, n], m++]; m]; Position[Abs @ Differences @ Array[kempner, 500], 1] // Flatten
%Y Cf. A002034, A346212.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jul 10 2021
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