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A306238 The smallest integer k such that floor(n!/k) is an odd number. 1
1, 1, 2, 2, 7, 7, 11, 13, 11, 11, 19, 13, 37, 17, 19, 17, 19, 19, 31, 41, 23, 23, 31, 31, 37, 29, 31, 29, 31, 31, 37, 37, 53, 37, 53, 37, 41, 41, 61, 41, 43, 43, 47, 61, 47, 47, 53, 53, 53, 53, 59, 53, 61, 61, 59, 67, 59, 59, 83, 61, 73, 67, 67, 89, 67, 67, 83, 79, 71, 71, 83 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is usually smaller than 2*n, but there are exceptions, such as n = 0, 12, 19.

Are there any other exceptions?

Conjecture: for n > 1, a(n) is a prime.

a(n) > n if n > 3. - Robert Israel, Mar 04 2019

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

For any k >= 4, a(A040976(k)) = A000040(k).

EXAMPLE

4! = 24, for k = 1, 2, 3, 4, 5, 6, floor(24/k) are even numbers, floor(24/7) = 3 is an odd number. So a(4) = 7.

MAPLE

f:= proc(n) local k, t;

  t:= n!;

  for k from 1 while floor(t/k)::even do od:

  k

end proc:

map(f, [$0..100]); # Robert Israel, Mar 04 2019

PROG

(PARI) a(n) = {k=1; m=n!; while(floor(m/k)%2==0, k++); k; }

CROSSREFS

Cf. A000040, A000142 (k!), A040976.

Sequence in context: A054085 A021443 A045923 * A318086 A244049 A271229

Adjacent sequences:  A306235 A306236 A306237 * A306239 A306240 A306241

KEYWORD

nonn

AUTHOR

Jinyuan Wang, Mar 01 2019

STATUS

approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)