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A178969 Last nonzero decimal digit of (10^10^n)! 0
8, 2, 6, 4, 2, 2, 6, 2, 6, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

It is possible to find a(10) using the program from the second Bomfim link, or a similar GMP program. Reserve 312500001 words instead of 31250001. Use a computer with at least 6 GB of RAM. - Washington Bomfim, Jan 06 2011

LINKS

Table of n, a(n) for n=0..9.

W. Bomfim, A property of the last non-zero digit of factorials

W. Bomfim, C program

FORMULA

From Washington Bomfim, Jan 06 2011: (Start)

a(n) = A008904(10^(10^n)).

a(n) = A008904(10^(10^n)) = A008904(2^(10^n)), if n > 0.

a(0) = 8, if n >= 1, with

N = 10^n, 2^N represented in base 5 as (a_h, ... ,a_0)5,

t = sum{i = h, h-1, ... , 0} (a_i even),

x = sum{i=h, h-1, ... , 1}(sum{k=h, h-1, ... , i}(a_i)),

z = (x + t/2) mod 4, and y = 2^z,

a(n) = 6(y mod 2) + y(1-(y mod 2)).

(End)

MATHEMATICA

f[n_] := Mod[6Times @@ (Rest[FoldList[{ 1 + #1[[1]], #2!2^(#1[[1]]#2)} &, {0, 0}, Reverse[IntegerDigits[n, 5]]]]), 10][[2]]; (* Jacob A. Siehler *) Table[ f[10^10^n], {n, 0, 4}]

PROG

(PARI)\\ L is the list of the N digits of 2^(10^n) in base 5.

\\ With 2^(10^n) in base 5 as (a_h, ... , a_0)5,

\\ L[1] = a_0, ... , L[N] = a_h.

convert(n)={n=2^(10^n); x=n; N=floor(log(n)/log(5)) + 1;

L = listcreate(N);

while(x, n=floor(n/5); r=x-5*n; listput(L, r); x=n; );

L; N

};

print("0 8"); for(n=1, 5, print1(n, " "); convert(n); q=0; t=0; x=0; forstep(i=N, 2, -1, a_i=L[i]; q+=a_i; x+=q; t+=a_i*(1-a_i%2); ); a_i=L[1]; t+=a_i*(1-a_i%2); z=(x+t/2)%4; y=2^z; an=6*(y%2)+y*(1-(y%2)); print(an)); \\ Washington Bomfim, Jan 06 2011

CROSSREFS

Cf. A008904, A173670

Sequence in context: A228818 A195845 A093207 * A019660 A021125 A234015

Adjacent sequences:  A178966 A178967 A178968 * A178970 A178971 A178972

KEYWORD

nonn,base,bref,more

AUTHOR

Robert G. Wilson v, Jan 01 2011

EXTENSIONS

a(9) from Washington Bomfim, Jan 06 2011

STATUS

approved

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Last modified March 23 18:13 EDT 2019. Contains 321433 sequences. (Running on oeis4.)