Sequences

Cycle class sequence c(n) (the number of true cycles of length n in which a certain node is included) for zeolite VSV = VPI-7 Na26H6[Zn16Si56O144].44H2O starting from a T3 atom.

Cycle class sequence c(n) (the number of true cycles of length n in which a certain node is included) for zeolite WEI = Weinebeneite Ca4[Be12P8O32(OH)8].16H2O starting from a T1 atom.

Cycle class sequence c(n) (the number of true cycles of length n in which a certain node is included) for zeolite WEI = Weinebeneite Ca4[Be12P8O32(OH)8].16H2O starting from a T2 atom.

Cycle class sequence c(n) (the number of true cycles of length n in which a certain node is included) for zeolite YUG = Yugawaralite Ca2[Al4Si12O32].8H2O starting at a T1 atom.

Cycle class sequence c(n) (the number of true cycles of length n in which a certain node is included) for zeolite YUG = Yugawaralite Ca2[Al4Si12O32].8H2O starting from a T2 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for square lattice.

From an asymptotic expansion for Pi.

Let Dedekind's psi(m) = product of (p+1)p^(e-1) for primes p, where p^e is a factor of m. Iterating psi(m) eventually results in a number of form 2^a*3^b. a(n) is the smallest number that requires n steps to reach such a number.

Let Dedekind's psi(m) = product of (p+1)p^(e-1) for primes p, where p^e is a factor of m. Iterating psi(m) eventually results in a number of form 2^a*3^b. a(n) is the number of steps to reach such a number.

A self-descriptive sequence: positions of vowels in "one, three, seven,...".

A self-descriptive sequence: positions of consonants in "zero, two, four, ...".

Erroneous version of A006558.

First run of n consecutive integers with same number of divisors ends at a(n).

Number of recursive calls needed to compute the n-th Fibonacci number F(n), starting with F(1) = F(2) = 1.

Incorrect version of A035010.

Megaperfect numbers: numbers n where A019294(n) = min {m: n divides sigma^(m) (n)} increases to a record; sigma^(m) means apply the sum-of-divisors function m times.

Records in A019294, number of iterations of the sigma function to reach a multiple of the starting value.

Numbers j such that sigma(sigma(j)) = k*j for some k.

Superperfect numbers: numbers k such that sigma(sigma(k)) = 2*k where sigma is the sum-of-divisors function (A000203).

Let sigma_m(n) be result of applying the sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m(n) = k*n; sequence gives log_2 of the (2,2)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,3)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,4)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,6)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,7)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,8)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,9)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,10)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,11)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,12)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,13)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,14)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (3,k)-perfect numbers.

Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (4,k)-perfect numbers.

Number (> 0) of iterations of sigma (A000203) required to reach a multiple of n when starting with n.

a(n) = sigma(sigma(...(sigma(n))...)) / n, where sigma (A000203) is iterated until a multiple of n is reached.

Values of n for which exp(Pi*sqrt(n)) is very close to an integer.

Integers k such that abs(e^(Pi*sqrt(n)) - k) < 0.01 for some n.

Number of balls in pyramid with base either a regular hexagon or a hexagon with alternate sides differing by 1 (balls in hexagonal pyramid of height n taken from hexagonal close-packing).

First n elements of Thue-Morse sequence A010059 read as a binary number.

First n elements of Thue-Morse sequence A010060 read as a binary number.

Binomial transform of Thue-Morse sequence A010059.

Binomial transform of Thue-Morse sequence A010060.

"Pascal sweep" for k=2: draw a horizontal line through the 1 at C(k,0) in Pascal's triangle; rotate this line and record the sum of the numbers on it (excluding the initial 1).

"Pascal sweep" for k=3: draw a horizontal line through the 1 at C(k,0) in Pascal's triangle; rotate this line and record the sum of the numbers on it (excluding the initial 1).

"Pascal sweep" for k=4: draw a horizontal line through the 1 at binomial(k,0) in Pascal's triangle; rotate this line and record the sum of the numbers on it (excluding the initial 1).

"Pascal sweep" for k=5: draw a horizontal line through the 1 at C(k,0) in Pascal's triangle; rotate this line and record the sum of the numbers on it (excluding the initial 1).

First time that the Grundy function G(x) for "subtract-a-Fibonacci-number" takes the value n.

Number of "bifix-free" words of length n over a three-letter alphabet.

Number of "bifix-free" words of length n over a four-letter alphabet.

Number of words of length n (n >= 1) over a two-letter alphabet having a minimal period of size n-1.