Sequences

Start with n; if prime, skip; repeatedly sum prime factors (counted with multiplicity) and add 1, until reach 1, 6 or a prime.

Start with n; repeatedly sum prime factors (counted with multiplicity) and add 1, until reach 1, 6 or a prime.

Start with n; if prime, stop; repeatedly sum squares of prime factors (counted with multiplicity), until reach 16 or a prime; set a(n) = 0 if no limit exists.

Start with n; repeatedly sum squares of prime factors (counted with multiplicity), until reach a prime p, then set a(n) = p; if reach a fixed point q, set a(n) = q; set a(n) = 0 if no limit exists.

Convert n from yards to meters.

Convert n from meters to yards.

Convert n from feet to meters.

Convert n from meters to feet.

Convert n from inches (") to centimeters (cm).

Convert n from centimeters (cm) to inches (").

Convert n from miles to kilometers (km).

Convert n from kilometers (km) to miles.

Convert n from pounds (lbs) to kilograms (kg).

Convert n from kilograms (kg) to pounds (lbs).

Convert n from degrees Celsius to nearest integer Fahrenheit.

Convert n from degrees Fahrenheit to nearest integer Celsius.

Convert n from nautical miles to statute miles.

Convert n from statute miles to nautical miles.

a(n) = n*(n + ceiling(2^n/12)).

If 2n = Sum 2^e_i, a(n) = Product 2^e_i.

If 2n = Sum 2^e_i, a(n) = Sum e_i.

Primes with record values of the least positive prime primitive root.

Numerator of n * Product_{d|n} (1 + 1/d).

Denominator of n * Product_{d|n} (1 + 1/d).

a(n) = Sum_{d divides n} phi(d)*phi(n/d).

Number of cusps of Gamma_1(n)\P_1(Q).

Genus of modular curve X_1(n).

a(n) = (p-5)(p-7)/24, where p=prime(n).

a(n) = Sum_{d|n} phi(d)^2.

a(n) = Product_{d|n} phi(d).

Number of symmetric types of (4,2n)-hypergraphs under action of complementing group C(4,2).

Numbers k such that the decimal expansion of k^3 contains k as a substring.

Substring of both its square and its cube.

a(n)^2 contains n-th prime as a substring.

Smallest square containing n-th prime as substring.

a(n)^3 contains n-th prime as a substring.

Smallest cube containing n-th prime as substring.

Smallest prime containing n-th square as substring.

Smallest prime containing n-th cube as substring.

Odd palindromes.

Even palindromes.

Palindromic in base 5.

Palindromic in base 6.

Palindromic in base 7.

Palindromic in base 9.

Numbers that are palindromic in base 11.

Numbers that are palindromic in base 12.

Numbers that are palindromic in base 13.

Numbers that are palindromic in base 14.

Numbers that are palindromic in base 15.