cp's OEIS Frontend

A272370 Number of geometrically inscriptible regular polygons with fewer than 2^n + 1 sides.

%I A272370 #23 Jul 29 2019 11:57:51
%S A272370 0,2,5,9,14,20,27,35,44,54,65,77,90,104,119,135,152,170,189,209,230,
%T A272370 252,275,299,324,350,377,405,434,464,495,527,559,591,623,655,687,719,
%U A272370 751,783,815,847,879,911,943,975,1007,1039,1071,1103,1135,1167,1199,1231,1263,1295
%N A272370 Number of geometrically inscriptible regular polygons with fewer than 2^n + 1 sides.
%C A272370 a(n) is the number of terms of A003401, except its first two degenerate case terms, that are less than 2^n + 1.
%H A272370 Jinyuan Wang, <a href="/A272370/b272370.txt">Table of n, a(n) for n = 1..10000</a>
%H A272370 Raymond Clare Archibald, <a href="http://www.jstor.org/stable/2974245">Remarks on Klein's "Famous Problems of Elementary Geometry"</a>, The American Mathematical Monthly, Vol. 21, No. 8 (Oct., 1914), pp. 247-259.
%H A272370 Leonard E. Dickson, <a href="http://dx.doi.org/10.1090/S0002-9904-1894-00195-5">On the number of inscriptible regular polygons</a>, Bull. Amer. Math. Soc. 3 (1894), 123-125.
%H A272370 Wilfrid Keller, <a href="http://www.prothsearch.com/fermat.html">Prime factors k.2^n + 1 of Fermat numbers F_m</a>
%F A272370 a(n) = (n-1)*(n+2)/2 if n < 32, otherwise 32*n-497 if n < 2^33.
%e A272370 For n=2, there are 2 such polygons, those with 3 and 4 sides, below 2^2+1 = 5.
%o A272370 (PARI) a(n) = if(n < 32, (n-1)*(n+2)/2, if(n < 2^33, 32*n-497));
%o A272370 (PARI) a(n) = {i = 2^n; j = 2*n - 2; k = 1; while(i > A045544(k) && k < 31, k++; j+=floor(log(i/A045544(k))/log(2))+1); j; } \\ _Jinyuan Wang_, Jul 29 2019
%Y A272370 Cf. A000051, A003401, A004169, A019434, A045544.
%K A272370 nonn
%O A272370 1,2
%A A272370 _Michel Marcus_, Apr 28 2016