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

%I A373100 #17 Jul 06 2024 23:47:36
%S A373100 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,
%T A373100 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
%N A373100 Last digit of n*2^n - 1.
%C A373100 This is a cyclic sequence of 20 numbers, using only 1,3,5,7 and 9 (4 times each).
%D A373100 Richard K. Guy (2004), Unsolved Problems in Number Theory (3rd ed.), New York: Springer Verlag, pp. section B20, ISBN 0-387-20860-7.
%H A373100 Wikipedia, <a href="https://en.wikipedia.org/wiki/Woodall_number">Woodall number</a>.
%H A373100 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1,1,1,-1,-1,1,0,-1,0,1).
%F A373100 a(n) = A010879(A003261(n)).
%F A373100 From _Chai Wah Wu_, Jul 06 2024: (Start)
%F A373100 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.
%F A373100 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)
%p A373100 lastDigit := proc(n)
%p A373100     return (n * 2^n - 1) mod 10;
%p A373100 end proc:
%p A373100 # Example usage
%p A373100 minN := 1; maxN := 10;
%p A373100 lastDigits := [seq(lastDigit(n), n = minN .. maxN)];
%p A373100 print(lastDigits);
%t A373100 lastDigit[n_] := Mod[n * 2^n - 1, 10]
%t A373100 (* Example usage *)
%t A373100 minN = 1; maxN = 10;
%t A373100 lastDigits = Table[lastDigit[n], {n, minN, maxN}]
%t A373100 Print[lastDigits]
%o A373100 (Python)
%o A373100 def last_digit(n):
%o A373100     return (n * 2**n - 1) % 10
%o A373100 # Example usage
%o A373100 min_n, max_n = 1, 10
%o A373100 last_digits = [last_digit(n) for n in range(min_n, max_n + 1)]
%o A373100 print(last_digits)
%o A373100 (PARI) a(n) = lift(Mod(n*2^n - 1, 10))
%Y A373100 Cf. A010879, A003261.
%Y A373100 Cf. A373098, A373099.
%K A373100 nonn,base,easy
%O A373100 1,2
%A A373100 _Javier Rodríguez Ríos_, May 23 2024