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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.)