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Period of powers of 7 mod 10^n.
2

%I #28 Feb 19 2024 10:49:48

%S 4,4,20,100,500,5000,50000,500000,5000000,50000000,500000000,

%T 5000000000,50000000000,500000000000,5000000000000,50000000000000,

%U 500000000000000,5000000000000000,50000000000000000,500000000000000000

%N Period of powers of 7 mod 10^n.

%C Essentially the same as A216099.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).

%F a(n) = 4*5^(n-2), 1 < n < 5.

%F a(n) = 5*10^(n-3), n >= 5.

%F a(n) = 2^(n-3)*5^(n-2) for n>4. a(n) = 10*a(n-1) for n>5. G.f.: 4*x*(125*x^4 +25*x^3 +5*x^2 +9*x -1) / (10*x -1). - _Colin Barker_, Sep 22 2013

%t Join[{4, 4, 20, 100}, NestList[10*# &, 500, 20]] (* _Paolo Xausa_, Feb 19 2024 *)

%Y Cf. A000420, A216156, A216099

%K nonn,base,easy

%O 1,1

%A _V. Raman_, Sep 02 2012