Sequences

a(n) = [ a(n-1)/a(1) + a(n-1)/a(2) + ... + a(n-1)/a(n-1) ] for n >= 3, with initial terms 1,2.

a(n) = [ a(n-1)/a(1) ] + [ a(n-1)/a(2) ] + ... + [ a(n-1)/a(n-1) ] for n >= 3, with initial terms 1,2.

a(n) = [ a(n-1)/a(1) + a(n-2)/a(2) + ... + a(1)/a(n-1) ], for n >= 3.

a(n) = [ a(n-1)/a(1) ] + [ a(n-2)/a(2) ] + ... + [ a(1)/a(n-1) ], for n >= 3.

a(n) = [ a(n-1)/a(1) + a(n-3)/a(3) + a(n-5)/a(5) + ... ], for n >= 3.

a(n) = [ a(n-1)/a(1) ] + [ a(n-3)/a(3) ] + [ a(n-5)/a(5) ] + ..., for n >= 3.

a(n) = [ a(n-1)/a(1) + a(n-1)/a(2) + ... + a(n-1)/a(n-1) ] for n >= 3, with initial terms 2,2.

a(n) = [ a(n-1)/a(1) ] + [ a(n-1)/a(2) ] + ... + [ a(n-1)/a(n-1) ] for n >= 3, with initial terms 2,2.

a(n) = [ a(n-1)/a(1) + a(n-2)/a(2) + ... + a(1)/a(n-1) ], for n >= 3.

a(n) = [ a(n-1)/a(1) ] + [ a(n-2)/a(2) ] + ... + [ a(1)/a(n-1) ], for n >= 3.

a(n) = [ a(n-1)/a(1) + a(n-3)/a(3) + a(n-5)/a(5) + ... ], for n >= 3.

a(n) = [ a(n-1)/a(1) ] + [ a(n-3)/a(3) ] + [ a(n-5)/a(5) ] + ..., for n >= 3.

a(n) = [ a(n-1)/a(1) + a(n-1)/a(2) + ... + a(n-1)/a(n-1) ] for n >= 3, with initial terms 2,1.

a(n) = [ a(n-1)/a(1) ] + [ a(n-1)/a(2) ] + ... + [ a(n-1)/a(n-1) ] for n >= 3, with initial terms 2,1.

a(n) = [ a(n-1)/a(1) + a(n-2)/a(2) + ... + a(1)/a(n-1) ], for n >= 3.

a(n) = [ a(n-1)/a(1) ] + [ a(n-2)/a(2) ] + ... + [ a(1)/a(n-1) ], for n >= 3.

a(n) = floor( a(n-1)/a(1) + a(n-3)/a(3) + a(n-5)/a(5) + ... ), for n >= 3 with a(1) = 1 and a(2) = 3.

a(n) = [ a(n-1)/a(1) ] + [ a(n-3)/a(3) ] + [ a(n-5)/a(5) ] + ..., for n >= 3.

The number of numbers [ [ ix ]jx ] that equal n, where i >= 1, j >= 1 and x=(1+sqrt(5))/2. a(n)=0 iff n is in Beatty sequence A001950.

The number of numbers [ [ ix ]jx ] that equal n, where i >= 1, j >= 1 and x=sqrt(2).

The number of numbers [ [ ix ]jx ] that equal n, where i >= 1, j >= 1 and x=sqrt(3).

The number of numbers [ [ ix ]jx ] that equal n, where i >= 1, j >= 1 and x=sqrt(5).

The number of numbers [ [ ix ]jx ] that equal n, where i >= 1, j >= 1 and x=e.

Numbers k such that prime(k) + prime(k+3) = prime(k+1) + prime(k+2).

Primes p=prime(k) such that prime(k) + prime(k+3) = prime(k+1) + prime(k+2).

n-th index k such that p(k) + p(k+4) = p(k+1) + p(k+3).

n-th prime p(k) such that p(k) + p(k+4) = p(k+1) + p(k+3).

n-th prime p(k) such that p(k) + p(k+5) = p(k+1) + p(k+4).

n-th prime p(k) such that p(k) + p(k+5) = p(k+1) + p(k+4).

n-th index k such that p(k) + p(k+6) = p(k+2) + p(k+4).

n-th prime p(k) such that p(k) + p(k+6) = p(k+2) + p(k+4).

n-th index k such that p(k) + p(k+9) = p(k+3) + p(k+6).

n-th prime p(k) such that p(k) + p(k+9) = p(k+3) + p(k+6).

Number of solutions to c(1)*prime(1) +...+ c(2n+1)*prime(2n+1) = 0, where c(i) = +-1 for i > 1, c(1) = 1.

Number of solutions to c(1)*prime(1) + ... + c(n)*prime(n) = 1, where c(i) = +-1 for i > 1, c(1) = 1.

Number of solutions to c(1)*prime(1) + ... + c(n)*prime(n) = 2, where c(i) = +-1 for i > 1, c(1) = 1.

Number of solutions to c(1)*prime(2) +...+ c(n)*prime(n+1) = 0, where c(i) = +-1 for i > 1, c(1) = 1.

Number of solutions to c(1)*prime(2)+...+c(n)*prime(n+1) = 1, where c(i) = +-1 for i > 1, c(1) = 1.

Number of solutions to c(1)*prime(2) + ... + c(n)*prime(n+1) = 2, where c(i) = +-1 for i > 1, c(1) = 1.

Number of solutions to c(1)*prime(3) + ... + c(n)*prime(n+2) = 0, where c(i) = +-1 for i>1, c(1) = 1.

Number of solutions to c(1)*prime(3)+...+c(n)*prime(n+2) = 1, where c(i) = +-1 for i>1, c(1) = 1.

Number of solutions to c(1)*prime(3)+...+c(n)*prime(n+2) = 2, where c(i) = +-1 for i>1, c(1) = 1.

Number of solutions to c(1)*prime(4) + ... + c(n)*prime(n+3) = 0, where c(i) = +-1 for i>1, c(1) = 1.

Number of solutions to c(1)*prime(4) + ... + c(n)*prime(n+3) = 1, where c(i) = +-1 for i>1, c(1) = 1.

a(n) = M(n) + m(n) for n >= 2, where M(n) = max{ a(i) + a(n-i): i = 1..n-1 }, m(n) = min{ a(i) + a(n-i): i = 1..n-1 }.

a(n) = M(n) - m(n) for n >= 2, where M(n) = max{ a(i) + a(n-i): i = 1..n-1 }, m(n) = min{ a(i) + a(n-i): i = 1..n-1 }.

The sequence m(n) in A022905.

The sequence M(n) in A022905.

The sequence m(n) in A022906.

The sequence M(n) in A022906.