Sequences

Fractional part of decimal expansion of sqrt(n) to 3 places.

a(n)/1000 gives sqrt(n) to 3 places after the decimal point.

a(n)/100000 gives sqrt(n) to 5 places after the decimal point.

a(n)/10000000 gives sqrt(n) to 7 places.

a(n)/100000 gives log_10(n) to 5 places.

a(n)/10000000 gives log_10(n) to 7 places.

Number of independent subsets of nodes of 3^n cube (P_3 X ... X P_3).

Number of independent subsets of nodes of 4^n cube (P_4 X ... X P_4).

Numbers k such that for some m, the sum of the first m k-gonal numbers is again a k-gonal number.

Number of different bracelets with 6 beads of at most n colors, allowing turning over.

Number of necklaces with n beads of 3 colors, allowing turning over.

Molien series for unitary 16-dimensional full Siegel modular group H_4 of order 48514675507200.

Number of nonisomorphic prime metrics on n points.

Numerical distance between m-th and (m+n)-th spheres in loxodromic sequence of spheres in which each 5 consecutive spheres are in mutual contact.

When squared gives number composed of digits {1,4,9}.

Squares composed of digits {1,4,6}.

When squared gives number composed of digits {1,4,6}.

Squares composed of digits {2,4,8}.

When squared gives number composed of digits {2,4,8} with each of these digits appearing at least once.

Number of independent subsets of 5^n cube (P_5 X ... X P_5).

Number of independent subsets of Hamming graph H(n,3).

Number of independent subsets of Hamming graph H(n,4).

Number of independent vertex sets of the n X n torus grid graph.

Number of letters in n (in "dotted" Hebrew).

Number of independent subsets of 4^n torus graph.

Number of ways to transform say (((((((ab)c)d)e)f)g)h) to (a(b(c(d(e(f(gh))))))) where there are n multiplications (hence n+1 variables) by repeatedly applying the one-way associative law ((xy)z) -> (x(yz)).

4-perfect (quadruply-perfect or sous-triple) numbers: sum of divisors of n is 4n.

a(n) = n^2 + n + 3.

a(n) = n^2 + n + 4.

a(n) = n^2 + n + 5.

a(n) = n^2 + n + 6.

a(n) = n^2 + n + 7.

a(n) = n^2 + n + 8.

a(n) = n^2 + n + 9.

Number of primitive polynomials of degree n over GF(4).

Numbers k >= 2 such that for some m >= 2, the sum of the first m k-gonal numbers is again a k-gonal number, excluding the parametric solution m = (k^2-4*k-2)/3 when k==2 (mod 3).

Odious primes: primes with odd number of 1's in binary expansion.

Numbers k such that the k-th prime has an odd number of 1's in its binary expansion.

Evil primes: primes with even number of 1's in their binary expansion.

Numbers k such that the k-th prime has an even number of 1's in its binary expansion.

Primes with even number of 1's in binary expansion such that next prime also has even number of 1's.

Numbers k such that the k-th prime has an even number of 1's in binary expansion and the (k+1)st prime also has an even number of 1's.

Primes with even number of 1's in binary expansion such that next prime has odd number of 1's.

Numbers k such that the k-th prime has an even number of 1's in its binary expansion and the (k+1)st prime has an odd number of 1's.

Primes with odd number of 1's in binary expansion such that next prime has even number of 1's.

n-th prime has odd number of 1's in binary expansion and (n+1)st prime has even number of 1's.

Primes with odd number of 1's in binary expansion such that next prime also has odd number of 1's.

n-th prime has odd number of 1's in binary expansion and (n+1)st prime also has odd number of 1's.

Minimal perimeter of polyomino with n square cells.

Number of ways of placing n labeled balls into n unlabeled (but 3-colored) boxes.