A008905 -id:A008905 - cp's OEIS frontend

A136754 Leading digit of n! in base 3.

1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Carl R. White, Jan 21 2008

			a(10) = 2 as 10! = 20211100210000_3 which has leading digit 2. - _David A. Corneth_, Jan 15 2021

David A. Corneth, Table of n, a(n) for n = 0..9999

Cf. A000142, A136690, A136755, A136756, A136757, A136758, A136759, A136760, A008905, A136761, A136762, A136763, A136764, A136765, A136766.

Table[First[IntegerDigits[n!,3]],{n,0,87}] (* Stefano Spezia, Aug 25 2022 *)

a(n, {b = 3}) = my(f = n!); f \ b^logint(f, b) \\ David A. Corneth, Jan 10 2021

Missing a(0)=1 inserted by David A. Corneth, Jan 10 2021

A136758 a(n) = leading digit of n! in base 7.

Original entry on oeis.org

1, 1, 2, 6, 3, 2, 2, 2, 2, 3, 4, 6, 1, 3, 6, 1, 4, 1, 3, 1, 4, 1, 5, 2, 1, 4, 2, 1, 5, 3, 2, 1, 5, 3, 2, 1, 1, 1, 5, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 1, 1, 1, 2, 3, 4, 5, 1, 1, 2, 3, 4, 1, 1, 2, 3, 5, 1, 2, 3, 5, 1, 2, 3, 6, 1, 3, 5, 1, 2, 4, 1, 2, 4, 1, 2, 5, 1, 2

Offset: 0

Carl R. White, Jan 21 2008

			a(10) = 4 as 10! = 42562410_7 which has leading digit 4. - _David A. Corneth_, Jan 15 2021

David A. Corneth, Table of n, a(n) for n = 0..9999

Cf. A000142, A136694, A136754, A136755, A136756, A136757, A136759, A136760, A008905, A136761, A136762, A136763, A136764, A136765, A136766.

f[n_]:=First[IntegerDigits[n!,7]]; lst={};Do[AppendTo[lst,f[n]],{n,0,2*5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)
First[IntegerDigits[#,7]]&/@(Range[0,100]!) (* Harvey P. Dale, Nov 23 2013 *)

a(n) = digits(n!, 7)[1]; \\ Michel Marcus, Jan 27 2015

A136759 a(n) = leading digit of n! in base 8.

Original entry on oeis.org

1, 1, 2, 6, 3, 1, 1, 1, 1, 1, 1, 2, 3, 5, 1, 2, 4, 1, 2, 6, 2, 5, 1, 5, 2, 6, 2, 1, 3, 1, 6, 3, 1, 6, 3, 1, 1, 4, 2, 1, 1, 5, 3, 2, 1, 1, 7, 5, 3, 2, 2, 1, 1, 1, 1, 7, 6, 5, 5, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 1, 1, 1, 1, 2, 2, 3, 4, 5, 7, 1, 1, 2, 2, 4, 5, 7, 1, 2, 2, 4, 6, 1, 1, 2, 4

Offset: 0

Carl R. White, Jan 21 2008

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

Cf. A000142, A136695, A136754, A136755, A136756, A136757, A136758, A136760, A008905, A136761, A136762, A136763, A136764, A136765, A136766.

f:= proc(n) local v; v:= n!; floor(v/8^floor(ilog2(v)/3)) end proc:
map(f, [$1..100]); # Robert Israel, Jun 07 2018

Array[IntegerDigits[#!, 8][[1]]&, 100, 0] (* Vincenzo Librandi, Jun 07 2018 *)

a(n) = digits(n!, 8)[1]; \\ Michel Marcus, Jan 27 2015

A136760 a(n) = leading digit of n! in base 9.

Original entry on oeis.org

1, 1, 2, 6, 2, 1, 8, 6, 6, 6, 6, 8, 1, 1, 2, 4, 8, 1, 3, 7, 1, 4, 1, 2, 7, 2, 6, 2, 7, 2, 8, 3, 1, 4, 1, 7, 3, 1, 6, 3, 1, 7, 3, 1, 1, 5, 3, 1, 1, 5, 3, 2, 1, 8, 5, 3, 2, 1, 1, 8, 6, 4, 3, 2, 2, 1, 1, 1, 1, 7, 6, 6, 5, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7, 8, 1, 1, 1, 1, 2, 2

Offset: 0

Carl R. White, Jan 21 2008

			a(10) = 6 as 10! = 6740700_9 which has leading digit 6. - _David A. Corneth_, Jan 15 2021

David A. Corneth, Table of n, a(n) for n = 0..9999

Cf. A000142, A136696, A136754, A136755, A136756, A136757, A136758, A136759, A008905, A136761, A136762, A136763, A136764, A136765, A136766.

f[n_]:=First[IntegerDigits[n!,9]]; lst={};Do[AppendTo[lst,f[n]],{n,0,2*5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)
IntegerDigits[#,9][[1]]&/@(Range[0,100]!) (* Harvey P. Dale, Jun 21 2021 *)

a(n) = digits(n!, 9)[1]; \\ Michel Marcus, Jan 27 2015

A136761 a(n) = leading digit of n! in base 11.

Original entry on oeis.org

1, 1, 2, 6, 2, 10, 5, 3, 2, 2, 2, 2, 2, 2, 3, 4, 6, 10, 1, 2, 4, 9, 1, 3, 7, 1, 3, 9, 2, 5, 1, 3, 1, 3, 9, 2, 9, 2, 9, 3, 1, 3, 1, 5, 1, 7, 2, 1, 4, 1, 9, 3, 1, 7, 3, 1, 8, 3, 1, 9, 4, 2, 1, 7, 3, 2, 1, 6, 3, 2, 1, 8, 4, 2, 1, 1, 7, 4, 3, 2, 1, 10, 6, 4, 3, 2, 1, 1, 9, 6, 5, 3, 2, 2, 1, 1, 1, 9, 7, 6

Offset: 0

Carl R. White, Jan 21 2008

			a(10) = 2 as 10! = 20594010_11 which has leading digit 2. - _David A. Corneth_, Jan 15 2021

David A. Corneth, Table of n, a(n) for n = 0..9999

Cf. A000142, A136697, A136754, A136755, A136756, A136757, A136758, A136759, A136760, A008905, A136762, A136763, A136764, A136765, A136766.

f[n_]:=First[IntegerDigits[n!,11]]; lst={};Do[AppendTo[lst,f[n]],{n,0,2*5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)
First[IntegerDigits[#,11]]&/@(Range[0,100]!) (* Harvey P. Dale, Feb 20 2013 *)

a(n) = digits(n!, 11)[1]; \\ Michel Marcus, Jan 27 2015

A136762 Leading digit of n! in base 12.

Original entry on oeis.org

1, 1, 2, 6, 2, 10, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 7, 1, 1, 3, 6, 1, 2, 5, 11, 2, 5, 1, 2, 7, 1, 4, 1, 3, 11, 2, 9, 2, 9, 2, 9, 2, 10, 3, 1, 4, 1, 6, 2, 9, 3, 1, 6, 2, 11, 4, 1, 9, 4, 1, 9, 4, 1, 10, 4, 2, 1, 6, 3, 1, 9, 4, 2, 1, 8, 4, 2, 1, 9, 5, 3, 1, 1, 7, 4, 2, 1, 1, 8, 5, 3, 2, 1, 11, 7, 5, 3

Offset: 0

Carl R. White, Jan 21 2008

Michael De Vlieger, Table of n, a(n) for n = 0..10368 (10368 = 6 * 12^3)

Cf. A000142, A136698, A136754, A136755, A136756, A136757, A136758, A136759, A136760, A008905, A136761, A136763, A136764, A136765, A136766.

f[n_]:=First[IntegerDigits[n!,12]]; lst={};Do[AppendTo[lst,f[n]],{n,0,2*5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)
a136762[n_Integer] := First[Select[IntegerDigits[n!, 12], # > 0 &]]; a136762 /@ Range[0, 144] (* Michael De Vlieger, Aug 13 2014 *)

A136763 a(n) = leading digit of n! in base 13.

Original entry on oeis.org

1, 1, 2, 6, 1, 9, 4, 2, 1, 12, 9, 8, 7, 7, 8, 9, 11, 1, 1, 2, 3, 5, 9, 1, 2, 4, 9, 1, 3, 7, 1, 3, 7, 1, 3, 10, 2, 6, 1, 4, 1, 3, 10, 2, 9, 2, 8, 2, 8, 2, 9, 2, 11, 3, 1, 4, 1, 7, 2, 11, 4, 1, 6, 2, 12, 4, 1, 9, 3, 1, 8, 3, 1, 8, 3, 1, 9, 4, 2, 12, 5, 2, 1, 8, 4, 2, 1, 7, 3, 2, 1, 7, 4, 2, 1, 9, 5, 3, 1, 1

Offset: 0

Carl R. White, Jan 21 2008

			a(10) = 9 as 10! = 9100926_13 which has leading digit 9. - _David A. Corneth_, Jan 15 2021

David A. Corneth, Table of n, a(n) for n = 0..9999

Cf. A000142, A136699, A136754, A136755, A136756, A136757, A136758, A136759, A136760, A008905, A136761, A136762, A136764, A136765, A136766.

Table[First[IntegerDigits[n!,13]],{n,0,100}] (* Harvey P. Dale, Dec 20 2015 *)

a(n) = digits(n!, 13)[1]; \\ Michel Marcus, Jan 27 2015

A136766 a(n) = leading digit of n! in base 16.

Original entry on oeis.org

1, 1, 2, 6, 1, 7, 2, 1, 9, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 5, 8, 12, 1, 2, 3, 6, 13, 1, 3, 6, 13, 1, 4, 9, 1, 3, 8, 1, 3, 10, 1, 4, 14, 2, 7, 1, 4, 14, 2, 9, 2, 7, 1, 5, 1, 4, 1, 4, 1, 3, 15, 4, 1, 4, 1, 5, 1, 6, 1, 7, 2, 10, 3, 15, 4, 1, 7, 2, 11, 3, 1, 6, 2, 11, 4, 1, 7, 2, 1, 5, 2, 12, 4, 1, 11

Offset: 0

Carl R. White, Jan 21 2008

			For n=5, 5! = 5*4*3*2*1 = 120 in base 10, which is 78 in hexadecimal (7*16 + 8*1), so a(5) = 7. - _Michael B. Porter_, Sep 20 2016

David A. Corneth, Table of n, a(n) for n = 0..9999 (first 1001 terms from Robert G. Wilson v)

Cf. A000142, A136702, A136754, A136755, A136756, A136757, A136758, A136759, A136760, A008905, A136761, A136762, A136763, A136764, A136765.

Array[ IntegerDigits[#!, 16][[1]] &, 1001, 0] (* Robert G. Wilson v, Sep 20 2016 *)
Table[Floor[#/16^Floor@ Log[16, #]] &[n!], {n, 0, 98}] (* Michael De Vlieger, Sep 20 2016 *)

a(n) = digits(n!, 16)[1]; \\ Michel Marcus, Jan 27 2015

A018799 Smallest nonnegative integer m such that m! begins with n in base 10.

Original entry on oeis.org

0, 2, 9, 8, 7, 3, 6, 14, 96, 27, 22, 5, 15, 42, 25, 89, 69, 76, 63, 16, 87, 113, 54, 4, 23, 30, 205, 85, 34, 28, 62, 164, 41, 245, 17, 9, 36, 128, 11, 8, 185, 53, 351, 73, 369, 118, 12, 265, 129, 7, 21, 38, 235, 66, 46, 258, 81, 597, 279, 43, 72, 13, 559, 18, 203, 120, 311

Offset: 1

David W. Wilson

Record high values are m = 0, 2, 9, 14, 96, 113, 205, 245, 351, 369, 597, ... (see A279089); these occur, respectively, at n = 1, 2, 3, 8, 9, 22, 27, 34, 43, 45, 58, ... (see A279090). - Jon E. Schoenfield, Jan 30 2017

The existence of such m for each n was proven by Maxfield in 1970. The first 999 terms of this sequence were calculated by Southard in 1983. - Amiram Eldar, Dec 18 2018

			Since no factorial below 96! ~ 9.91*10^149 starts with 9, we have a(9) = 96. Similarly, 16 first appears as the leading digits of 89! ~ 1.65*10^136 and hence a(16) = 89. - _Lekraj Beedassy_, Oct 31 2010 and _Robert G. Wilson v_, Nov 05 2010

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (terms 1..1000 from David W. Wilson).
John E. Maxfield, A Note on N!, Mathematics Magazine, Vol. 43. No. 2 (1970), pp. 64-67.
Laura Southard, Investigations on Maxfield's Theorem, Pi Mu Epsilon Journal, Vol. 7, No. 8 (1983), pp. 493-495, alternative link.

Cf. A018854.
Apart from leading term, identical to A076219.
Cf. A000142, A008905, A279089, A279090.

f[n_] := Block[{k = 0, m}, While[ m = Max[0, Floor@ Log[10, k! ] - Floor@ Log[10, n]]; (k! - Mod[k!, 10^m])/10^m != n, k++ ]; k]; Array[f, 67] (* Robert G. Wilson v, Nov 05 2010 *)

A018799(n)={ local( F=1,k=0 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=10)); k} \\ M. F. Hasler, Feb 01 2009

A136755 a(n) = leading digit of n! in base 4.

Original entry on oeis.org

1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 2, 3, 1, 2, 3, 1, 3, 1, 3, 1, 3, 1, 1, 2, 1, 3, 2, 1, 3, 2, 1, 1, 3, 2, 1, 1, 1, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 1, 1, 1, 2, 2, 3, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1

Offset: 0

Carl R. White, Jan 21 2008

Cf. A000142, A136691, A136754, A136756, A136757, A136758, A136759, A136760, A008905, A136761, A136762, A136763, A136764, A136765, A136766.

f[n_]:=First[IntegerDigits[n!,4]]; lst={};Do[AppendTo[lst,f[n]],{n,0,2*5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)

a(n) = digits(n!, 4)[1]; \\ Michel Marcus, Jan 27 2015

cp's OEIS Frontend

A136754 Leading digit of n! in base 3.

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A136758 a(n) = leading digit of n! in base 7.

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A136759 a(n) = leading digit of n! in base 8.

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A136760 a(n) = leading digit of n! in base 9.

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A136761 a(n) = leading digit of n! in base 11.

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A136762 Leading digit of n! in base 12.

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A136763 a(n) = leading digit of n! in base 13.

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A136766 a(n) = leading digit of n! in base 16.

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