Sequences

Smallest power of 5 that begins with n.

5^a(n) is smallest power of 5 beginning with n.

Smallest power of 6 that begins with n.

6^a(n) is smallest power of 6 beginning with n.

Smallest power of 7 that begins with n.

7^a(n) is smallest power of 7 beginning with n.

Smallest power of 8 that begins with n.

8^a(n) is smallest power of 8 beginning with n.

Smallest power of 9 that begins with n.

9^a(n) is smallest power of 9 beginning with n.

Smallest fifth power that begins with n.

a(n)^5 is smallest fifth power beginning with n.

Smallest sixth power that begins with n.

a(n)^6 is smallest sixth power beginning with n.

Smallest seventh power that begins with n.

a(n)^7 is smallest seventh power beginning with n.

Smallest eighth power that begins with n.

a(n)^8 is smallest eighth power beginning with n.

Smallest ninth power that begins with n.

a(n)^9 is smallest ninth power beginning with n.

Smallest tenth power that begins with n.

a(n)^10 is smallest tenth power beginning with n.

Least nonsquare having square residues for all moduli 2 through n.

Squares using at most two distinct digits, not ending in 0.

Squares using no more than two distinct digits.

Waring's problem: least positive integer requiring maximum number of terms when expressed as a sum of positive n-th powers.

Waring's problem: historical upper bounds on A079611, as stated in a web page in 1996.

Numbers which are not the sum of seven nonnegative cubes.

Numbers whose shortest representation as a sum of positive cubes requires exactly 8 cubes.

Numbers whose smallest expression as a sum of positive cubes requires exactly 7 cubes.

Number of positive knots with n crossings.

Number of ways to write 1/n as a sum of exactly 2 unit fractions.

Blasius sequence: from coefficients in expansion of solution to Blasius's equation in boundary layer theory.

Numbers k such that sigma(k)/phi(k) sets a new record.

Weight distribution of [512,130,64] third-order Reed-Muller code.

a(n) = ( a(n-1)*a(n-7) + a(n-4)^2 ) / a(n-8); a(0) = ... = a(7) = 1.

Weight distribution of [512,382,16] 9th-order Reed-Muller (or RM) code.

Theta series of 14-dimensional lattice of det 3^7 and minimal norm 2.

Smallest positive integer not representable as the sum of at most n distinct numbers of form 2^a*3^b.

Sums of two distinct powers of 2.

Central hexanomial coefficients: largest coefficient of (1 + x + ... + x^5)^n.

a(n+2) = 5*a(n+1) - 3*a(n).

Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(1,5).

Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(1,6).

Duplicate of A024537.

Define the Shallit sequence S(a_0,a_1) by a_{n+2} is the least integer > a_{n+1}^2/a_n for n >= 0. This is S(2,6).

Define the sequence S(a_0,a_1) by a_{n+2} is the least integer such that a_{n+2}/a_{n+1} > a_{n+1}/a_n for n >= 0. This is S(2,7).

Define sequence S(a_0,a_1) by a_{n+2} is least integer such that a_{n+2}/a_{n+1}>a_{n+1}/a_n for n >= 0. This is S(3,4).

Define the sequence S(a_0,a_1) by a_{n+2} is the least integer such that a_{n+2}/a_{n+1}>a_{n+1}/a_n for n >= 0. This is S(3,6).

Pisot sequence L(4,5).