Sequences

Numbers k such that s(k) + s(k+1) + ... + s(k+3) = t(k) + t(k+1) + ... + t(k+3).

Numbers k such that s(k) + s(k+1) + ... + s(k+4) = t(k) + t(k+1) + ... + t(k+4).

Numbers k such that s(k) + s(k+1) + ... + s(k+6) = t(k) + t(k+1) + ... + t(k+6).

Numbers k such that s(k) + s(k+1) + ... + s(k+7) = t(k) + t(k+1) + ... + t(k+7).

Numbers n such that s(n)+s(n+1)+...+s(n+10) = t(n)+t(n+1)+...+t(n+10).

Numbers k such that s(k) + s(k+1) + ... + s(k+14) = t(k) + t(k+1) + ... + t(k+14).

Coefficients of iterated exponential function defined by y(x) = x^y(x) for e^-e < x < e^(1/e), expanded about x=1.

Triangular array in which n-th row consists of the numbers 1^1, 2^2, ... n^n.

Odd k for which k+2^m is composite for all m < k.

Largest proper substring of n-th prime that is prime (0 if none).

Largest proper substring of 2^n that is a power of 2 (0 if none).

Base-2 digital convolution sequence.

Base 3 digital convolution sequence.

Base 4 digital convolution sequence.

Base 5 digital convolution sequence.

Base 6 digital convolution sequence.

Base 7 digital convolution sequence.

Base 8 digital convolution sequence.

Base 9 digital convolution sequence.

Base 10 digital convolution sequence.

a(n) = lcm(n,n+1,n+2).

Least positive m such that n! + m is prime.

Least nonnegative m such that n! - m is prime.

a(n) = (10^n + 1)^2.

Sum of squares of coefficients in full expansion of (z1+z2+...+zn)^n.

a(n+1) = a(n) + sum of squares of digits of a(n).

Convolution of natural numbers n >= 1 with Fibonacci numbers F(k), k >= 3.

Palindromic primes n such that the period of 1/n is a palindrome.

Period of 1/n in sequence A033938.

a(n) = 10^n mod 7.

Number of ways A002808(n) can be properly factored into 2 integers.

Positive integers with at least 3 prime factors (counted with multiplicity).

Sum of coefficients of a polynomial associated to a family of digraphs.

Compare partial sums of A033881 and A033884; this is the sequence of common terms.

Record highs in A033885 (3n - sum of divisors of n).

Values of n corresponding to A033945.

Smallest primitive root (in absolute value) of n-th prime.

Numbers that have a primitive root (the multiplicative group modulo n is cyclic).

Positive integers that do not have a primitive root.

Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.

Write 1,2,... in a clockwise spiral; sequence gives numbers on positive x axis.

Write 1,2,... in a clockwise spiral on a square lattice, writing each digit at a separate lattice point, starting with 1 at the origin and 2 at x=0, y=-1; sequence gives the numbers on the positive x-axis.

Write 0,1,2,... in a clockwise spiral on a square lattice, writing each digit at a separate lattice point, starting with 0 at the origin and 1 at x=0, y=-1; sequence gives the numbers on the positive x-axis.

Second 10-gonal (or decagonal) numbers: n*(4*n+3).

a(n) = sum of the remainders when the n-th prime is divided by primes up to the (n-1)-th prime.

a(n) = prime(n) + A033955(n).

Duplicate of A031131.

In the '3x+1' problem, these values for the starting value set new records for number of steps to reach 1.

Record number of steps to reach 1 in '3x+1' problem, corresponding to starting values in A033958.

Convolution of natural numbers n >= 1 with Fibonacci numbers F(k), k >= 4.