Sequences

Lexicographically earliest increasing sequence of nonnegative numbers that contains no arithmetic progression of length 9.

Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 9.

Lexicographically earliest increasing sequence of nonnegative numbers that contains no arithmetic progression of length 10.

Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 10.

a(n) is the (conjectured) maximal exponent k such that n^k does not contain a digit zero in its decimal expansion.

a(n)^n is the least n-th power containing every digit.

Least n-th power containing every digit.

Numbers of the form x^2 + 4*y^2.

Numbers of form x^2 + 5 y^2.

Numbers of form x^2 + 7y^2.

Numbers of form x^2 + 8 y^2.

Numbers of form x^2 + 9 y^2.

Numbers of form x^2 + 10 y^2.

Numbers of the form 2*x^2 + 5*y^2.

Numbers of form 2 x^2 + 7 y^2.

Numbers of form 2 x^2 + 9 y^2.

Numbers of form 3*x^2 + 4*y^2.

Numbers of form 3 x^2 + 5 y^2.

Numbers of form 3*x^2 + 7*y^2.

Numbers of form 3 x^2 + 8 y^2.

Numbers of form 3 x^2 + 10 y^2.

Numbers of form 4 x^2 + 5 y^2.

Numbers of form 4 x^2 + 7 y^2.

Numbers of form 4 x^2 + 9 y^2.

Numbers of form 5 x^2 + 6 y^2.

Numbers of form 5 x^2 + 7 y^2.

Numbers of form 5 x^2 + 8 y^2.

Numbers of form 5 x^2 + 9 y^2.

Numbers of form 6 x^2 + 7 y^2.

Numbers of form 7 x^2 + 8 y^2.

Numbers of form 7 x^2 + 9 y^2.

Numbers of form 7 x^2 + 10 y^2.

Numbers of the form 8*x^2 + 9*y^2.

Numbers of form 9 x^2 + 10 y^2.

Pisot sequence E(2,3).

Let a,b,c,...k be all divisors of n; a(n) = (a+1)*(b+1)*...*(k+1).

Number of divisors of A019505(n).

a(n) = 5*a(n-1) - 2*a(n-2), with a(0)=2, a(1)=9.

Expansion of (1-3*x)/(1-5*x).

Numbers k such that k + sum of its prime factors = (k+1) + sum of its prime factors.

Pisot sequences E(3,5), P(3,5).

Expansion of (1+x^10)/((1-x)*(1-x^2)*(1-x^3)*(1-x^5)).

Take the sequence of natural numbers (A000027) and reverse successive subsequences of lengths 1,3,5,7,...

Pisot sequences E(3,10), P(3,10).

a(n) = n + 4.

Pisot sequences L(4,6), E(4,6).

Pisot sequences E(4,8), L(4,8), P(4,8), T(4,8).

Pisot sequences E(4,9), P(4,9).

Pisot sequence E(4,10).

a(n) = n + 5.