

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
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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] (* JeanFrançois 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



