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A122988 Number of possible arrangements of the last three digits of x^n for all x>0 (leading zeros omitted). 3
1, 1000, 159, 505, 52, 105, 102, 505, 52, 505, 22, 505, 52, 505, 102, 105, 52, 505, 102, 505, 12, 505, 102, 505, 52, 25, 102, 505, 52, 505, 22, 505, 52, 505, 102, 105, 52, 505, 102, 505, 12, 505, 102, 505, 52, 105, 102, 505, 52, 505, 6, 505, 52, 505, 102, 105, 52 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Only possible values are {1, 4, 6, 12, 22, 25, 52, 102, 105, 159, 505, 1000}. - Robert G. Wilson v, Sep 27 2006.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Square Number..

Eric Weisstein's World of Mathematics, Cubic Number..

FORMULA

a(n)=1 for n=0 only,

a(n)=4 for n=100*k, k=1..inf.,

a(n)=6 for n=100*k-50, k=1..inf.,

a(n)=12 for n=20*k, k=1..inf. except if k == 0 (mod 5),

a(n)=22 for n=20*k-10, k=1..inf. except if k == 3 (mod 5),

a(n)=25 for n=50*k-25, k=1..inf.,

a(n)=52 for n=4*k, k=1..inf. except if k == 0 (mod 5),

a(n)=102 for n=4*k-2, k=2..inf. except if k == 3 (mod 5),

a(n)=105 for n=10*k-5, k=1..inf. except if k == 3 (mod 5),

a(n)=159 for n=2 only,

a(n)=505 for n=2*k-1, k=2..inf. except if k == 3 (mod 5) and

a(n)=1000 for n=1 only.

EXAMPLE

a(0) = 1 because the last three digits of x^0 are always 001 (just one possibility). a(100)=4 because the last three digits of x^100 can be 000, 001, 376 or 625 (which is four possibilities)

MATHEMATICA

f[n_] := Length@ Union@ PowerMod[ Range@1000, n, 1000]; Table[ f@n, {n, 0, 56}] (* Robert G. Wilson v *)

CROSSREFS

Cf. A122986, A122987, A000578, A006716, A027676.

Sequence in context: A038459 A072990 A112023 * A069536 A126820 A033421

Adjacent sequences:  A122985 A122986 A122987 * A122989 A122990 A122991

KEYWORD

base,nonn

AUTHOR

Sergio Pimentel, Sep 22 2006

EXTENSIONS

Edited and extended by Robert G. Wilson v, Sep 27 2006

STATUS

approved

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Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)