Sequences

Baum-Sweet cubic sequence.

Triangle read by rows; row 0 is 0; the n-th row for n>0 contains the coefficients in the expansion of (1-x)*(1+x)^(n-1).

Reading binary expansion from right to left, run lengths strictly decrease.

Numbers n with property that reading binary expansion from right to left (from least significant to most significant), run lengths do not increase.

Numbers n with property that, reading binary expansion of n from right to left, run lengths strictly increase.

Numbers n with property that reading binary expansion from right to left (least significant to most significant), run lengths do not decrease.

Prime pentadecet homolog of {11,13,17,...,61,67}.

Conjecturally, largest k with no prime in [ k, k(1+1/n) ].

Let n = p_1*p_2*...*p_k be the prime factorization of n, with the primes sorted in descending order. Then a(n) = 2^(p_1 - 1)*3^(p_2 - 1)*...*A000040(k)^(p_k - 1).

Numbers whose sum of proper (or aliquot) divisors is a prime.

Greedy sequence such that no term is the average of four others.

Triangle in which row n has the first n digits of sqrt(n) (truncated).

Triangle in which row n lists the first n digits of sqrt(n) (rounded).

Position of start of first occurrence of prime(n) after the decimal point in expansion of Pi.

a(1) = 8; a(n) = least k with d(k) = a(n-1), where d(k) is the number of divisors of k.

Number of B-trees of order 4 with n leaves.

Skew Fibonacci-Pascal triangle read by rows.

Prime closest to e^n.

Primes of the form 666*n + 1.

Numbers n such that 666*n + 1 is prime.

Number of combinations of n objects taken pi(n) at a time.

Total number of prime parts in all partitions of n.

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

Least k such that 4*n*k-1 is a prime.

Least k such that 2^n+1+k is a prime.

Least k such that 2^n+1-k is a prime.

Number of primes between n and 3n.

Number of primes between n and 4n+1.

Least k such that 4*n*k+1 is a prime.

Number of odd nonprimes < (2n+1)^2.

Number of quadratic residues mod n for some n (A000224 sorted and duplicates removed).

2-White numbers (take power 2, sum 2-digit groups to get same number).

3-white numbers: partition digits of n^3 into blocks of 3 starting at right; then sum of these 3-digit numbers equals n.

4-white numbers: partition digits of n^4 into blocks of 4 starting at right; sum of these 4-digit numbers equals n.

5-white numbers: partition digits of n^5 into blocks of 5 starting at right; sum of these 5-digit numbers equals n.

Numbers that are not the number of quadratic residues mod n for any n.

Starting at n, "say what you see"; sequence gives number of primes obtained before first composite number appears.

Number of pairs {i,j}, i>1, j>1, such that ij < n^2.

Smallest number with two distinct prime factors both of length n.

Numbers n such that product of n with sum of next n consecutive integers is palindromic.

Palindromic product of some n with sum of next n consecutive integers.

a(n)-th prime is the smallest prime containing exactly n 0's.

Smallest prime containing exactly n 0's.

a(n)-th prime is the smallest prime containing exactly n 1's.

Smallest prime containing exactly n 1's.

a(n)-th prime is the smallest prime containing exactly n 2's.

Smallest prime containing exactly n 2's.

a(n)-th prime is the smallest prime containing exactly n 3's.

Smallest prime containing exactly n 3's.

a(n)-th prime is the smallest prime containing exactly n 4's.