A136702 -id:A136702 - cp's OEIS frontend

A136701 Final nonzero digit of n! in base 15.

1, 1, 2, 6, 9, 8, 3, 6, 3, 12, 3, 3, 6, 3, 12, 12, 12, 9, 12, 3, 9, 9, 3, 9, 6, 9, 9, 3, 9, 6, 12, 12, 9, 12, 3, 12, 12, 9, 12, 3, 3, 3, 6, 3, 12, 6, 6, 12, 6, 9, 12, 12, 9, 12, 3, 6, 6, 12, 6, 9, 6, 6, 12, 6, 9, 9, 9, 3, 9, 6, 3, 3, 6, 3, 12, 9, 9, 3, 9, 6, 12, 12, 9, 12, 3, 12, 12, 9, 12, 3, 3, 3, 6

Offset: 0

Carl R. White, Jan 16 2008

From Robert Israel, Jun 08 2018: (Start)
For n >= 6, a(n) is 3, 6, 9 or 12.
For k >= 2, a(5*k) = a(5*k+1) = a(5*k+3). (End)

			6! = 720 decimal = 330 quindecimal, so a(6) = 3.

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

Cf. A000142, A136690, A136691, A136692, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136700, A136702.

a:= 1: b:= 0: R[0]:= 1:
for n from 1 to 100 do
   alpha:= padic:-ordp(n,3);
   beta:= padic:-ordp(n,5);
   a:= a * n/3^alpha/5^beta;
   b:= b + alpha - beta;
   R[n]:= a * 3 &^ b mod 15;
od:
seq(R[n],n=0..100); # Robert Israel, Jun 08 2018

nzd[x_]:=If[x[[-1,1]]==0,x[[-2,1]],x[[-1,1]]]; Table[nzd[Split[IntegerDigits[n!,15]]],{n,0,100}] (* Harvey P. Dale, Jul 11 2023 *)

A136693 Final nonzero digit of n! in base 6.

Original entry on oeis.org

1, 1, 2, 1, 4, 2, 2, 2, 4, 4, 4, 2, 4, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 4, 4, 2, 4, 4, 2, 2, 2, 4, 4, 4, 2, 4, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 2, 4, 2, 2, 4, 4, 4, 2, 4, 4, 2, 4, 4, 2, 2, 2, 4, 4, 4, 2, 4, 4, 2, 2, 2, 4, 4, 4, 2, 4, 4, 2, 2, 2, 4, 2

Offset: 0

Carl R. White, Jan 16 2008

			6! = 720 decimal = 3200 senary, so a(6) = 2.

Cf. A000142, A136690, A136691, A136692, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136700, A136701, A136702.

nzd6[n_]:=Module[{c=IntegerExponent[n!,6]},IntegerDigits[n!,6] [[-(c+1)]]]; Array[nzd6,100,0] (* Harvey P. Dale, Sep 02 2015 *)

A136700 Final nonzero digit of n! in base 14.

Original entry on oeis.org

1, 1, 2, 6, 10, 8, 6, 10, 10, 6, 4, 2, 10, 4, 4, 4, 8, 10, 12, 4, 10, 8, 8, 2, 6, 10, 8, 6, 12, 12, 10, 2, 8, 12, 2, 12, 12, 10, 2, 8, 12, 2, 6, 6, 12, 8, 4, 6, 8, 2, 2, 4, 12, 6, 2, 12, 6, 6, 12, 8, 4, 6, 8, 8, 8, 2, 6, 10, 8, 6, 2, 2, 4, 12, 6, 2, 12, 10, 10, 6, 4, 2, 10, 4, 10, 10, 6, 4, 2, 10, 4

Offset: 0

Carl R. White, Jan 16 2008

			6! = 720 decimal = 396 quatridecimal, so a(6) = 6.

Cf. A000142, A136690, A136691, A136692, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136701, A136702.

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

A136774 n! never ends in this many 0's in base 16.

Original entry on oeis.org

62, 94, 110, 118, 126, 158, 174, 182, 190, 206, 214, 222, 230, 238, 254, 286, 302, 310, 318, 334, 342, 350, 358, 366, 382, 398, 406, 414, 422, 430, 446, 454, 462, 478, 510, 542, 558, 566, 574, 590, 598, 606, 614, 622, 638, 654, 662, 670, 678, 686, 702, 710

Offset: 1

Carl R. White, Jan 21 2008

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Cf. A000142, A136766, A136702, A000966, A055938, A096346, A136767, A136768, A136769, A136770, A136771, A136772, A136773.

is(n)=my(t=4*n+2,s=1-hammingweight(n)); while(s<0, s+=valuation(t+=2,2)); s>3 \\ Charles R Greathouse IV, Sep 22 2016

Conjecture: a(n) ~ 16n. This holds with probability 1 in a random model. - Charles R Greathouse IV, Sep 22 2016

cp's OEIS Frontend

A136701 Final nonzero digit of n! in base 15.

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A136693 Final nonzero digit of n! in base 6.

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A136700 Final nonzero digit of n! in base 14.

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

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A136774 n! never ends in this many 0's in base 16.

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