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 A332558 a(n) is the smallest k such that n*(n+1)*(n+2)*...*(n+k) is divisible by n+k+1. 15
 4, 3, 2, 3, 4, 5, 4, 3, 5, 4, 6, 5, 6, 5, 4, 7, 6, 5, 4, 3, 6, 7, 6, 5, 4, 8, 7, 6, 6, 5, 8, 7, 6, 5, 4, 8, 7, 6, 5, 7, 6, 5, 10, 9, 8, 9, 8, 7, 6, 9, 8, 7, 6, 5, 4, 6, 12, 11, 10, 9, 8, 7, 6, 7, 6, 5, 12, 11, 10, 9, 8, 7, 6, 5, 8, 7, 6, 11, 10, 9, 8, 7, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is a multiplicative analog of A332542. a(n) always exists because one can take k to be 2^m - 1 for m large. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 David A. Corneth, PARI program J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004.14000 [math.NT], April 2020. FORMULA a(n) = A061836(n) - 1 for n >= 1. a(n + 1) >= a(n) - 1. a(n + 1) = a(n) - 1 mostly. - David A. Corneth, Apr 14 2020 MAPLE f:= proc(n) local k, p;   p:= n;   for k from 1 do     p:= p*(n+k);     if (p/(n+k+1))::integer then return k fi   od end proc: map(f, [\$1..100]); # Robert Israel, Feb 25 2020 MATHEMATICA a[n_] := Module[{k, p = n}, For[k = 1, True, k++, p *= (n+k); If[Divisible[p, n+k+1], Return[k]]]]; Array[a, 100] (* Jean-François Alcover, Jun 04 2020, after Maple *) PROG (PARI) a(n) = {my(r=n*(n+1)); for(k=2, oo, r=r*(n+k); if(r%(n+k+1)==0, return(k))); } \\ Jinyuan Wang, Feb 25 2020 (PARI) \\ See Corneth link CROSSREFS Cf. A061836 (k+1), A332559 (n+k+1), A332560 (the final product), A332561 (the quotient). For records, see A333532 and A333533 (and A333537), which give the records in the essentially identical sequence A061836. Additive version: A332542, A332543, A332544, A081123. "Concatenate in base 10" version: A332580, A332584, A332585. Sequence in context: A084255 A247847 A076576 * A183197 A245459 A001368 Adjacent sequences:  A332555 A332556 A332557 * A332559 A332560 A332561 KEYWORD nonn,look AUTHOR Scott R. Shannon and N. J. A. Sloane, Feb 24 2020 STATUS approved

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)