Sequences

Squares that remain square when the digit 1 is appended.

Squares that remain square when the digit 4 is appended.

Squares that remain square when the digit 6 is appended.

Squares that remain square when the digit 9 is appended.

Signature sequence of 1/sqrt(2) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of 1/sqrt(3) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of sqrt(5) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of 1/sqrt(5) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of sqrt(7) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of 1/sqrt(7) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of sqrt(2/3) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of sqrt(3/2) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of e (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of 1/e (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of e^2 (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of 1/e^2 (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of sqrt(6) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of 1/sqrt(6) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of sqrt(e).

Signature sequence of 1/sqrt(e) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of sqrt(8) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of 1/sqrt(8) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of Pi (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Signature sequence of 1/Pi (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).

Number of cycles of function f(x) = 3x mod n.

Number of cycles of function f(x) = 4x mod n.

Number of cycles of function f(x) = 5x mod n.

Number of cycles of function f(x) = 6x mod n.

Number of cycles of function f(x) = 7x mod n.

Number of cycles of function f(x) = 8x mod n.

Number of cycles of function f(x) = 9x mod n.

Number of cycles of function f(x) = 10x mod n.

Numbers k such that prime(k) == 1 (mod k).

Numbers k such that prime(k) == 2 (mod k).

Numbers k such that prime(k) == 3 (mod k).

Numbers k such that prime(k) == 4 (mod k).

Numbers k such that prime(k) == 5 (mod k).

Numbers k such that prime(k) == 6 (mod k).

Numbers k such that prime(k) == 7 (mod k).

Numbers k such that prime(k) == 8 (mod k).

Numbers k such that prime(k) == 9 (mod k).

Numbers k such that prime(k) == 10 (mod k).

Number of cycles of function f(x) = x^2 mod n.

Number of cycles of function f(x) = x^3 mod n.

Number of cycles of function f(x) = x^4 mod n.

Number of cycles of function f(x) = x^5 mod n.

Number of cycles of function f(x) = x^6 mod n.

Number of cycles of function f(x) = x^7 mod n.

Number of cycles of function f(x) = x^8 mod n.

Number of cycles of function f(x) = x^9 mod n.