Sequences

Numbers that do not divide 2^k + 1 for any k>0.

Primes p such that order of 2 mod p (=A007733(p)) is even.

Primes p such that multiplicative order of 2 modulo p is odd.

Order of 2 modulo the n-th prime.

Number of new fractions m/n < 1, where (m,n)=1 and "new" means the value of m*n has not occurred before.

Erroneous version of A027435.

Inverse of 658th cyclotomic polynomial.

a(1) = 1, a(n) = Sum_{k=1..n-1} Sum_{d|k} a(d).

Inverse of 660th cyclotomic polynomial.

G.f.: (1+x)*(1+x^3)*(1+x^5)*(1+x^7)*(1+x^9)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^8)*(1-x^10)).

Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of alternating group A_7 subset A_8 acting on polynomial ring F_2[ x_1,y_1,z_1,w_1 ].

Inverse of 663rd cyclotomic polynomial.

Smallest prime factor of greatest proper divisor of n.

Inverse of 665th cyclotomic polynomial.

The infinite Fibonacci word (start with 1, apply 1->2, 2->21, take limit).

Inverse of 667th cyclotomic polynomial.

First differences of A001468.

Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of Lyons group.

G.f.: (1+x^3)^2/((1-x^2)*(1-x^3)*(1-x^4)).

Inverse of 671st cyclotomic polynomial.

Fix 0; exchange even and odd numbers.

The Collatz or 3x+1 function: a(n) = n/2 if n is even, otherwise (3n+1)/2.

In the sequence of positive integers add 1 to each prime number.

In the sequence of positive integers subtract 1 from each prime number.

In sequence of positive integers add 1 to first prime and subtract 1 from 2nd prime; add 1 to 3rd prime and subtract 1 from 4th prime and so on.

In sequence of prime numbers add 1 to first prime, 3rd prime, fifth prime, ... then subtract 1 from 2nd prime, fourth prime, sixth prime and so on.

In sequence of odd primes add 1 to first prime, 3rd prime, 5th prime, ... then subtract 1 from 2nd prime, fourth prime, sixth prime and so on.

a(n) = n-th prime + n.

a(n) = prime(n)-n, the number of nonprimes less than prime(n).

a(n) = n + prime(n+1).

Inverse of 682nd cyclotomic polynomial.

a(n) = prime(n) - (n-1).

In sequence of prime numbers add 1 to first number, 2 to 3rd number, 3 to 5th number, ... then subtract 1 from 2nd number, 2 from 4th number, 3 from 6th number and so on.

a(n) = prime(n+1) - (-1)^n*ceiling(n/2).

Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of Q_8.

Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of universal W-group W(3).

Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of universal W-group W(4).

Inverse of 689th cyclotomic polynomial.

Inverse of 690th cyclotomic polynomial.

Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of universal W-group W(5).

Number of multiplications to compute n-th power by the Chandah-sutra method.

Inverse of 693rd cyclotomic polynomial.

Expansion of ((theta_2)^4+(theta_3)^4)/Delta_24.

Expansion of ((theta_2)^4+(theta_3)^4)/(Delta_24)^2.

Expansion of ((theta_2)^4 + (theta_3)^4) / eta(z/2)^4.

Inverse of 697th cyclotomic polynomial.

a(4n) = 0, a(4n+2) = 1, a(2n+1) = a(n).

Coefficients of the modular function J = j - 744.

The regular paper-folding (or dragon curve) sequence. Alphabet {1,2}.

The regular paper-folding (or dragon curve) sequence. Alphabet {2,1}.