Sequences

Numbers k such that in k and k^3 the parity of digits alternates.

Cubes such that in n and n^(1/3) the parity of digits alternates.

Solutions x of 2*uphi(x)=x, where uphi is the unitary phi function (A047994).

Numbers n such that uphi(sigma(n)) = n, where the uphi is the unitary phi function A047994.

Numbers m such that uphi(sigma(m)) = 2m, where the unitary phi function (A047994) is defined by: if x = p1^r1*p2^r2*p3^r3*... then uphi(x) = (p1^r1 - 1)*(p2^r2 - 1)*(p3^r3 - 1)*...

Number of strokes in Chinese characters for n; also number of strokes in Japanese kanji characters for n.

Continued fraction expansion of the Champernowne constant 0.1234567891011121314...

Continued fraction for Copeland-Erdős constant 0.235711... (concatenate primes).

Decimal expansion of the real positive number x such that Gamma(x) is a minimum.

Let c be the point at which Gamma(x), x>0, is minimized; sequence gives continued fraction for c.

Decimal expansion of real number y such that y = Gamma(x) is a minimum.

Let c be the point at which Gamma(x), x>0, is minimized; sequence gives continued fraction for Gamma(c).

Differences p(i)-p(j) between primes, sorted in numerical order.

Squares composed of digits {1,2,3}.

When squared gives number composed of digits {1,2,3}.

Squares composed of digits {4,5,6}.

When squared gives number composed of digits {4,5,6}.

Decimal expansion of LambertW(1): the solution to x*exp(x) = 1.

Quarter-squares squared: A002620^2.

a(n) = (n^7 - n)/42.

Expansion of (eta(q) / eta(q^7))^4 in powers of q.

McKay-Thompson series of class 3B for the Monster group with a(0) = -12.

McKay-Thompson series of class 7A for the Monster group with a(0) = 10.

Expansion of eta(q) * eta(q^3) * eta(q^5) * eta(q^15) in powers of q.

Coefficients in expansion of E_2*E_4/(E_6*j) in powers of 1/j.

a(n) = 3*a(n-1) + a(n-2) - a(n-3) for n >= 3, a(0)=1, a(1)=2, a(2)=7.

Expansion of eta(q) * eta(q^2) * eta(q^7) * eta(q^14) in powers of q.

Expansion of q^(-1/2) * eta(q) * eta(q^2) * eta(q^3) * eta(q^6) in powers of q.

Expansion of eta(q)*eta(q^2)*eta(q^4)*eta(q^8).

Binary Champernowne sequence (or word): write the numbers 0,1,2,3,4,... in base 2 and juxtapose.

Scaled Chebyshev U-polynomial evaluated at sqrt(5)/2.

Scaled Chebyshev U-polynomial evaluated at sqrt(6)/2.

Let S = squares; a(0)=0; a(n) = smallest m such that m - a(i) is not in S for any i < n.

a(0)=0; a(n) is the smallest m such that m - a(i) is not a triangular number for any i < n.

a(n) = 3*a(n-1) + 3*a(n-2), a(0)=0, a(1)=1.

Distinct elements occurring in triangle of Eulerian numbers (sorted).

McKay-Thompson series of class 3A for the Monster group with a(0) = 42.

a(n) = n^((n+1)^(n+2)).

Expansion of x * Product_{k>=1} (1 - x^k) * (1 - x^(23*k)).

Expansion of q^(-1/2) * eta(q) * eta(q^11) in powers of q.

Expansion of eta(q^3)*eta(q^21).

Expansion of q^(-1/4) * eta(q) * eta(q^5) in powers of q.

Expansion of q^(-1/6) * eta(q) * eta(q^3) in powers of q.

Expansion of q^(-1/8) * eta(q) * eta(q^2) in powers of q.

Expansion of q^(-1/2) * eta(q)^2 * eta(q^5)^2 in power of q.

Expansion of q^(-1/3) * eta(q)^2 * eta(q^3)^2 in powers of q.

Expansion of eta(q)^2 * eta(q^2) * eta(q^4) * eta(q^8)^2 in powers of q.

Expansion of q^(-1/2) * (eta(q) * eta(q^3))^3 in powers of q.

Expansion of (eta(q) * eta(q^2) * eta(q^3) * eta(q^6))^2 in powers of q.

Expansion of (eta(q) * eta(q^5))^4 in powers of q.