A376478 - OEIS

%I #11 Nov 14 2024 08:20:23

%S 1,2,3,9,27,81,243,729,2187,6561,19683,59049,177147,531441,1594323,

%T 4782969,14348907,43046721,129140163,387420489,1162261467,3486784401,

%U 10460353203,31381059609,94143178827,282429536481,847288609443,2541865828329,7625597484987,22876792454961

%N a(1) = 1, a(2) = 2, and a(n) = 3^(n-2) for n > 2.

%C Graham's conjecture: also numbers k such sigma(k) - k = floor(k/2). See Guy.

%D R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B2.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (3).

%F a(n) = 3*a(n-1) for n > 3.

%F G.f.: (1 - x - 3*x^2)/(1 - 3*x).

%F E.g.f.: (2 + exp(3*x) + 3*x)/3.

%t LinearRecurrence[{3},{1,2,3},30]

%o (Python)

%o def A376478(n): return n if n<3 else 3**(n-2) # _Chai Wah Wu_, Nov 13 2024

%Y Cf. A000244, A140429, A001065, A004526.

%K nonn,easy

%O 1,2

%A _Stefano Spezia_, Sep 24 2024