login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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