A069261 Denominators of the Egyptian fraction for the fractional part of Feigenbaum's constant, 4.6692...

2, 6, 395, 303319, 131209492876, 45596605913248081159007, 34243827483200809826686815883136413405197711755, 111445370519459209554489628949586784217535791333333948765270067675689059510906528783799426730444

Offset: 1

Author

Christopher Lund (clund(AT)san.rr.com), Apr 14 2002

Keywords

• frac
• nonn

Comments

The next term in the series, a(9), is ~ 10^190.

The sequence gives the denominators for the fractional part of delta only. One could prefix four 1's in order to get (sum of reciprocals) = delta.

Links

• Kevin Ryde, Table of n, a(n) for n = 1..10

Crossrefs

Cf. A006890 (Feigenbaum's constant), A069544 (continued fraction).

Programs

PARI

t=delta-4/*from A006890, or use: t=contfracpnqn(A069544); t[1,1]/t[2,1]*/; for(i=1,8,print1(1\t+1",");t-=1/(1\t+1)) \\ Requires delta to 93 decimals or A069544 to 90 terms (up to [...,1,1,4]) to get a(7) correctly, 180 terms for a(8). - M. F. Hasler, Apr 30 2018

Formula

a(n) = ceiling(1/(delta - 4 - Sum_{0 < i < n} 1/a(i))) is the smallest integer such that 4 + Sum_{i=1..n} 1/a(i) < delta = 4.6620... - M. F. Hasler, Apr 30 2018

Extensions

Edited by M. F. Hasler, Apr 30 2018