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A269225 Smallest k such that k! > 2^n. 1
2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27, 27, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

EXAMPLE

a(7) = 6 because 6! = 720 > 2^7 = 128, but 5! = 120 < 128.

MATHEMATICA

a[n_] := Block[{v=2^n, k=1}, While[++k! <= v]; k]; Array[a, 93, 0] (* Giovanni Resta, Jul 11 2016 *)

PROG

(Python)

def a269225():

...k = 1

...f = 1

...p = 1

...n = 0

...while True:

......while f<=p:

.........k += 1

.........f *= k

......yield k

......p *= 2

......n += 1

(PARI) a(n)=localprec(19); my(t=log(2)*n, x=ceil(solve(k=1, n/2+5, lngamma(k+1)-t))); while(x!<=2^n, x++); x \\ Charles R Greathouse IV, Jul 12 2016

CROSSREFS

Cf. A003070, A067850, A258782.

Sequence in context: A031247 A062575 A073188 * A217713 A047740 A137687

Adjacent sequences:  A269222 A269223 A269224 * A269226 A269227 A269228

KEYWORD

nonn,easy

AUTHOR

Christian Perfect, Jul 11 2016

STATUS

approved

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Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)