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A373100
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Last digit of n*2^n - 1.
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2
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1, 7, 3, 3, 9, 3, 5, 7, 7, 9, 7, 1, 5, 5, 9, 5, 3, 1, 1, 9, 1, 7, 3, 3, 9, 3, 5, 7, 7, 9, 7, 1, 5, 5, 9, 5, 3, 1, 1, 9, 1, 7, 3, 3, 9, 3, 5, 7, 7, 9, 7, 1, 5, 5, 9, 5, 3, 1, 1, 9, 1, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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This is a cyclic sequence of 20 numbers, using only 1,3,5,7 and 9 (4 times each).
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REFERENCES
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Richard K. Guy (2004), Unsolved Problems in Number Theory (3rd ed.), New York: Springer Verlag, pp. section B20, ISBN 0-387-20860-7.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,1,1,-1,-1,1,0,-1,0,1).
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FORMULA
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a(n) = a(n-2) - a(n-4) + a(n-5) + a(n-6) - a(n-7) - a(n-8) + a(n-9) - a(n-11) + a(n-13) for n > 13.
G.f.: x*(-9*x^12 - x^11 + 8*x^10 - 2*x^9 - 13*x^8 + 2*x^7 + 9*x^6 - 6*x^5 - 7*x^4 + 4*x^3 - 2*x^2 - 7*x - 1)/((x - 1)*(x^4 + x^3 + x^2 + x + 1)*(x^8 - x^6 + x^4 - x^2 + 1)). (End)
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MAPLE
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lastDigit := proc(n)
return (n * 2^n - 1) mod 10;
end proc:
# Example usage
minN := 1; maxN := 10;
lastDigits := [seq(lastDigit(n), n = minN .. maxN)];
print(lastDigits);
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MATHEMATICA
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lastDigit[n_] := Mod[n * 2^n - 1, 10]
(* Example usage *)
minN = 1; maxN = 10;
lastDigits = Table[lastDigit[n], {n, minN, maxN}]
Print[lastDigits]
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PROG
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(Python)
def last_digit(n):
return (n * 2**n - 1) % 10
# Example usage
min_n, max_n = 1, 10
last_digits = [last_digit(n) for n in range(min_n, max_n + 1)]
print(last_digits)
(PARI) a(n) = lift(Mod(n*2^n - 1, 10))
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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