A373100 Last digit of n*2^n - 1.

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

Offset

1,2

Comments

This is a cyclic sequence of 20 numbers, using only 1,3,5,7 and 9 (4 times each).

References

Richard K. Guy (2004), Unsolved Problems in Number Theory (3rd ed.), New York: Springer Verlag, pp. section B20, ISBN 0-387-20860-7.

Links

Table of n, a(n) for n=1..62.

Wikipedia, Woodall number.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,1,1,-1,-1,1,0,-1,0,1).

Formula

a(n) = A010879(A003261(n)).

From Chai Wah Wu, Jul 06 2024: (Start)

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)

Maple

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);

Mathematica

lastDigit[n_] := Mod[n * 2^n - 1, 10]
(* Example usage *)
minN = 1; maxN = 10;
lastDigits = Table[lastDigit[n], {n, minN, maxN}]
Print[lastDigits]

Prog

(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))

Crossrefs

Cf. A010879, A003261.

Cf. A373098, A373099.

Sequence in context: A154019 A011299 A225453 * A153858 A200294 A169813

Adjacent sequences: A373097 A373098 A373099 * A373101 A373102 A373103

Keyword

nonn,base,easy

Author

Javier Rodríguez Ríos, May 23 2024

Status

approved