A359457 -id:A359457 - cp's OEIS frontend

A359458 a(n) = A001911(n)*A003266(n+2).

0, 2, 18, 180, 2640, 59280, 2096640, 118067040, 10659448800, 1548438091200, 362727075110400, 137200338475200000, 83862700757150515200, 82876486430812314240000, 132456397879190606981760000, 342431262483097194433458432000, 1432128704666605129972385934336000

Offset: 0

A.H.M. Smeets, Jan 03 2023

Terms of the form 10^a(n)-1 for n>0 occur as large terms in the continued fraction expansion A359457 of the constant A359456.

Winston de Greef, Table of n, a(n) for n = 0..95

Cf. A000045, A001911, A003266, A359456, A359457.

a(n) = (Sum_{i = 1..n} Fibonacci(i+1)) * (Product_{i = 1..n} Fibonacci(i+1)), with Fibonacci(k) = A000045(k).

A359838 Continued fraction for binary expansion of A359456 interpreted in base 2.

Original entry on oeis.org

0, 1, 3, 3, 1, 2, 1, 262143, 3, 1, 3, 3, 1, 1532495540865888858358347027150309183618739122183602175, 4, 3, 1, 3, 262143, 1, 2, 1, 3, 3, 1

Offset: 0

A.H.M. Smeets, Jan 14 2023

The continued fraction of the number obtained by reading A359456 as a binary fraction.
Except for the first term, the only values that occur in this sequence are 1, 2, 3, 4 and values 2^A359458(m) - 1 for m > 2. The probabilities of occurrence P(a(n) = k) are given by:
P(a(n) = 1) = 1/3,
P(a(n) = 2) = 1/12,
P(a(n) = 3) = 1/3,
P(a(n) = 4) = 1/12 and
P(a(n) = 2^A359458(m)-1) = 1/(3*2^m) for m > 1.

Cf. A014710, A317538, A317539, A359456, A359458.

Cf. A359457 (in base 10).

a(n) = 1 if and only if n in A317538.
a(n) = 2 if and only if n in {24*m - 19 | m > 0} union {24*m - 4 | m > 0}.
a(n) = 3 if and only if n in A317539.
a(n) = 4 if and only if n in {12*m - 3*A014710(m-1) + 5 | m > 0}
a(n) = 2^A359458(m)-1 if and only if n in {3*2^(m-1)*(1+k*4) + 1 | k >= 0} union {3*2^(m-1)*(3+k*4) | k >= 0} for m > 1.

cp's OEIS Frontend

A359458 a(n) = A001911(n)*A003266(n+2).

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