Sequences

Smallest prime containing exactly n 4's.

a(n)-th prime is the smallest prime containing exactly n 5's.

Smallest prime containing exactly n 5's.

a(n)-th prime is the smallest prime containing exactly n 6's.

Smallest prime containing exactly n 6's.

a(n)-th prime is the smallest prime containing exactly n 7's.

Smallest prime containing exactly n 7's.

a(n)-th prime is the smallest prime containing exactly n 8's.

Smallest prime containing exactly n 8's.

a(n)-th prime is the smallest prime containing exactly n 9's.

Smallest prime containing exactly n 9's.

Squares which are the sum of twin prime pairs.

Numbers k such that (6*k)^2 is the sum of a twin prime pair.

Numbers that are the product of a pair of twin primes.

Number of eutactic lattices in dimension n.

Palindromes which are the sum of a twin prime pair.

Decimal expansion of upper limit of - 1^(1/1) + 2^(1/2) - 3^(1/3) + ... .

In ternary expansion of n, reading from right to left, digits occur in order ...,0,1,2,0,1,2,...

In ternary expansion of n, reading from left to right, digits occur in order ...,0,1,2,0,1,2,...

In ternary expansion of n, reading from right to left, successive runs of the digits occur in order ...,0,1,2,0,1,2,...

In ternary expansion of n, reading from left to right, successive runs of the digits occur in order ...,0,1,2,0,1,2,...

Primes of the form k!!! + 1.

Numbers k such that k!!! + 1 is prime (0 is included by convention).

Positive integers not going to 1 under iterations of the map in A001281: n->3n-1 if n odd, n->n/2 if n even.

Beatty sequence for Pi^2.

Beatty sequence for sqrt(Pi).

Beatty sequence for e^(1/e).

Triangle read by rows: T(n,k) is number of numbers x, 2^n <= x < 2^(n+1), with k prime factors (counted with multiplicity).

Lexicographically earliest strictly increasing decimal autovarious sequence: a(n) = number of distinct n-digit endings (left-zero-padded) of terms in the sequence.

Lexicographically earliest strictly increasing base-2 autovarious sequence: a(n) = number of distinct a(k) mod 2^n (written in base 2).

Lexicographically earliest strictly increasing base 3 autovarious sequence: a(n) = number of distinct a(k) mod 3^n (written in base 3).

Number of triples {i,j,k}, i>1, j>1, k>1, such that i*j*k < n^3.

"Sloping binary representation" of Fibonacci numbers, slope = +1.

"Sloping binary representation" of Lucas numbers (A000032), slope = +1.

"Sloping binary representation" of powers of 3 (A000244), slope = -1.

Periodic vertical binary vectors computed for powers of 3: a(n) = Sum_{k=0 .. (2^n)-1} (floor((3^k)/(2^n)) mod 2) * 2^k.

Periodic vertical binary vectors of powers of 3, starting from bit-column 2 (halved).

Sequence A037093 shown in octal.

Sequence A037094 shown in octal.

Lexically first set of (even) numbers, beginning with 4, such that for any two different terms, a(i) + a(j) + 1 is prime.

Trajectory of 3 under map n->7n+1 if n odd, n->n/2 if n even.

Trajectory of 3 under map n->9n+1 if n odd, n->n/2 if n even.

Trajectory of 3 under map n->11n+1 if n odd, n->n/2 if n even.

Trajectory of 3 under map n->13n+1 if n odd, n->n/2 if n even.

Trajectory of 3 under map n->15n+1 if n odd, n->n/2 if n even.

Trajectory of 3 under map n->17n+1 if n odd, n->n/2 if n even.

Trajectory of 3 under map n->19n+1 if n odd, n->n/2 if n even.

Trajectory of 3 under map n->21*n+1 if n odd, n->n/2 if n even.

Trajectory of 3 under map n->23n+1 if n odd, n->n/2 if n even.

Trajectory of 3 under map n->25n+1 if n odd, n->n/2 if n even.