A325300 - OEIS

%I #18 Dec 31 2020 11:11:15

%S 6,9,15,20,24,31,35,42,49,59,63,72,76,84,95,106,110,121,125

%N a(n) is the number of faces of the stepped pyramid with n levels described in A245092.

%C To calculate a(n) consider that levels greater than n do not exist.

%C The shape of the n-th level of the pyramid allows us to know if n is prime (see the Formula section).

%C For more information about the sequences that we can see in the pyramid see A262626.

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr05.jpg">Perspective view of the pyramid (first 16 levels)</a>

%F a(n) = A325301(n) - A325302(n) + 2 (Euler's formula).

%F a(n) = A323645(n) + 3.

%F a(n) = a(n-1) + 4 iff n is a prime > 3 (A215848).

%e For n = 1 the first level of the stepped pyramid (starting from the top) is a cube, and a cube has six faces, so a(1) = 6.

%Y Cf. A325301 (number of edges), A325302 (number of vertices).

%Y Cf. A196020, A215848, A235791, A236104, A237270, A237271, A237591, A237593, A245092, A262626, A299692, A323645, A323648.

%K nonn,more

%O 1,1

%A _Omar E. Pol_, Apr 16 2019