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A076157 Continued fraction expansion for c=sum_{k>=0} 1/2^(k!). 4
1, 3, 1, 3, 4, 4095, 1, 3, 3, 1, 3, 4722366482869645213695, 1, 2, 1, 3, 3, 1, 4095, 4, 3, 1, 3, 3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290175 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Observation: if b(k) denotes the sequence of all elements of the continued fraction for c, b(k) = 4095 if k==6 or 19 (mod 24); b(k) = 4722366482869645213695 if k==12 or 37 (mod 48); .... If b(k) is not congruent to 5 (mod 10), it seems that b(k) = 1,2,3 or 4 only.

Conjecture: a(3*2^n) = -1 + 2^[(n+1)((n+2)!) ]. - Ralf Stephan, May 17 2005

LINKS

Rick L. Shepherd, Table of n, a(n) for n = 1..47

Rick L. Shepherd, Table of n, a(n) for n = 1..383 (has larger terms than b-files support)

FORMULA

c=1.2656250596046447753906250000000000007... = A076187.

PROG

(PARI)

{allocatemem(220000000);

default(realprecision, 1000000);

contfrac(suminf(k=0, 1/(2^(k!))))}

CROSSREFS

Cf. A076152, A076154, A076187.

Cf. A007400, A004200, A006466.

Sequence in context: A284619 A147549 A177355 * A087493 A118125 A143732

Adjacent sequences:  A076154 A076155 A076156 * A076158 A076159 A076160

KEYWORD

cofr,nonn

AUTHOR

Benoit Cloitre, Nov 02 2002

EXTENSIONS

More terms from Ralf Stephan, May 17 2005

b-file, a-file, PARI program, and corrected conjecture by Rick L. Shepherd, Jun 07 2013

STATUS

approved

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Last modified June 24 03:27 EDT 2021. Contains 345415 sequences. (Running on oeis4.)