Sequences

Erroneous version of A348211.

E.g.f. arcsin(log(x+1)/exp(x)).

Expansion of e.g.f. arctan(log(x+1)/exp(x)).

Expansion of e.g.f. arcsinh(log(x+1)/exp(x)).

E.g.f. arctanh(log(x+1)/exp(x)).

Expansion of e.g.f. sec(log(x+1)/exp(x)).

E.g.f. sech(log(x+1)/exp(x)).

Almost certainly an erroneous version of A317209.

Expansion of e.g.f. exp(arcsin(x)/exp(x)).

Numerator of [x^n] of the Taylor series log(arctan(x)/log(x+1)).

Expansion of e.g.f. exp(arctan(x)/exp(x)).

Expansion of e.g.f. of exp(arcsinh(x)/exp(x)).

Expansion of e.g.f. exp(arctanh(x)/exp(x)).

Minimal scope of an (n,2) difference triangle.

Minimal scope of an (n,3) difference triangle.

Minimal scope of an (n,4) difference triangle.

Minimal scope of an (n,5) difference triangle.

Maximal size of equidistant permutation array R(n,2).

Number of inequivalent Mendelsohn triple systems (MTS(n,1)) of order n and index 1.

Triangle formed in same way as Pascal's triangle (A007318) except 1 is added to central element in even-numbered rows.

Let P = 2*3*5*..*p_n = n-th primorial number (A002110), G = Z_2xZ_3x...xZ_{p_n}; a(n) = max{e in G} min{i : both e+i, e-i are relatively prime to P}.

Number of positions in game "Connect Four" (played on usual 6-row, 7-column board) after n moves, up to reflection.

Smallest positive number that can be written as sum of distinct Fibonacci numbers in n ways.

Smallest m such that 0!+1!+...+(m-1)! is divisible by n, or 0 if no such m exists.

Smallest m such that 1!+...+m! is divisible by 2n+1, or 0 if no such m exists.

Smallest prime p such that n divides one of f(p)-1, f(p) or f(p)+1, where f(p) is product of primes <= p, or 0 if no such p exists.

Number of rational plane curves of degree d passing through 3d-1 general points.

Smallest positive integer not the determinant of an n X n {0,1}-matrix.

a(n+1) = a(n)*(a(n)+1)/2.

Numbers k such that Phi(k,x) is a cyclotomic polynomial containing a coefficient with an absolute value greater than one.

Orders of cyclotomic polynomials containing a coefficient the absolute value of which is >= 3.

Orders of cyclotomic polynomials containing a coefficient the absolute value of which is >= 4.

Orders of cyclotomic polynomials containing a coefficient the absolute value of which is >= 5.

Smallest order of cyclotomic polynomial containing n or -n as a coefficient.

Irregular triangle read by rows: coefficients of cyclotomic polynomial Phi_n(x) (exponents in increasing order).

Irregular triangle of coefficients of cyclotomic polynomial Phi_n(x) (exponents in decreasing order).

a(n) = nextprime(2^n) - 2^n.

a(n) = nextprime(3^n)-3^n.

a(n) = nextprime(5^n) - 5^n.

a(n) = nextprime(6^n)-6^n.

a(n) = nextprime(7^n)-7^n.

a(n) = nextprime(4^n)-4^n.

Difference between 2^n and the nearest prime less than or equal to 2^n.

a(n) = 3^n - prevprime(3^n), where prevprime(x) is the largest prime < x.

a(n) = 5^n-prevprime(5^n).

a(n) = 4^n - prevprime(4^n).

a(n) = 6^n-prevprime(6^n).

7^n-prevprime(7^n).

Triangle of coefficients in expansion of (1+2*x)^n.

Triangle of coefficients in expansion of (1+3*x)^n.