Sequences

Denominator of density of integers with smallest prime factor prime(n).

a(n) = T(2n,n), where T(n,k) is in A037027.

Lexicographically earliest strictly increasing base 4 autovarious sequence: a(n) = number of distinct a(k) mod 4^n (written in base 4).

Lexicographically earliest strictly increasing base 5 autovarious sequence: a(n) = number of distinct a(k) mod 5^n (written in base 5).

Lexicographically earliest strictly increasing base 6 autovarious sequence: a(n) = number of distinct a(k) mod 6^n (written in base 6).

Lexicographically earliest strictly increasing base 7 autovarious sequence: a(n) = number of distinct a(k) mod 7^n (written in base 7).

Lexicographically earliest strictly increasing base 8 autovarious sequence: a(n) = number of distinct a(k) mod 8^n (written in base 8).

Lexicographically earliest strictly increasing base 9 autovarious sequence: a(n) = number of distinct a(k) mod 9^n (written in base 9).

Number of n-celled solid polyominoes (or free polycubes, allowing mirror-image identification).

Number of distinct n-digit suffixes of base 6 squares not containing digit 0.

E.g.f.: (1 + 15*x + (45/2)*x^2 + (5/2)*x^3)/(1 - 2*x)^(13/2).

Start with {1,2,...,n}, replace any two numbers a,b with |a^2-b^2|, repeat until single number k remains; a(n) = minimal value of k.

Beatty sequence for Feigenbaum's constant.

Beatty sequence for Brun's constant.

a(n) = Sum_{k=0..n} (k-n)^k.

a(n) = floor( sqrt(2*Pi)*n ) (a Beatty sequence).

A Beatty sequence: a(n) = floor(n*2^sqrt(2)).

Beatty sequence for Euler's constant (A001620).

Beatty sequence for cube root of 2.

Beatty sequence for 2*Pi.

Second earliest sequence of 6 primes according to the rules stipulated in A005150.

Third earliest sequence of 6 primes according to the rules stipulated in A005150.

From a subtractive Goldbach conjecture: odd primes that are not cluster primes.

From a subtractive Goldbach conjecture: cluster primes.

Pseudo Q-numbers.

Erroneous version of A134996.

Reflection of A037027: T(n,m) = U(n,n-m), m=0..n, where U is as in A037027.

Order of n (mod 7).

Order of n (mod 9).

Number of planar polyhexes with n cells and a single hole of size at least 2.

Number of planar polyhexes with n cells with at least two holes, all holes having size at least two.

Number of planar cata-polyhexes with n cells.

Hexagonal cata-condensed helicenes with n cells (non-planar cata-fused benzenoid hydrocarbons).

Number of planar n-hexes, or polyhexes (in the sense of A000228, so rotations and reflections count as the same shape) with at least one hole.

Number of n-celled helicenes without holes.

Number of n-celled helicenes with peri-fragments.

Number of polyhexes with n cells.

Number of 3-infinitary divisors of n: if n = Product p(i)^r(i) and d = Product p(i)^s(i), each s(i) has a digit a <= b in its ternary expansion everywhere that the corresponding r(i) has a digit b, then d is a 3-infinitary-divisor of n.

a(n) = max T(n,k), with T as in A037027.

Array of numbers used in exotic ternary numeration system, read by antidiagonals.

Bilateral directed animals in first and 8th octants.

Beatty sequence for e^Pi.

Beatty sequence for Pi^e.

a(n) = n! * Sum_{k=0..n-2} 1/k!.

a(n) = (n!/2) * Sum_{k=0..n-2} 1/k!.

a(n) = n! * Sum_{k=1..n-1} 1/k!.

a(n) = n! * Sum_{k=1..n-2} 1/k!.

a(n) = (n!/2)*Sum(1/k!, k=1..n-2).

a(n) = n*a(n-1) + 1, a(0) = 2.

Intersection of A003136 and A038590.