A076157 -id:A076157 - cp's OEIS frontend

A092910 a(n) is the (3n+2)-th component of the continued fraction for sum(k>=0,2^(-k!)).

3, 4, 3, 3, 2, 3, 4, 3, 2, 4, 3, 2, 3, 3, 4, 3, 2, 4, 3, 3, 2, 3, 4, 2, 3, 4, 3, 2, 3, 3, 4, 3, 2, 4, 3, 3, 2, 3, 4, 3, 2, 4, 3, 2, 3, 3, 4, 2, 3, 4, 3, 3, 2, 3, 4, 2, 3, 4, 3, 2, 3, 3, 4, 3, 2, 4, 3, 3, 2, 3, 4, 3, 2, 4, 3, 2, 3, 3, 4, 3, 2, 4, 3, 3, 2, 3, 4, 2, 3, 4, 3, 2, 3, 3, 4, 2, 3, 4, 3, 3, 2, 3, 4, 3, 2

Offset: 0

Benoit Cloitre, Apr 16 2004

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A007400, A076157, A088431.

a(n)=5-component(contfrac(sum(i=0,10,1/2^(2^i))),n+3)/2

(define (A092910 n) (- 5 (* 1/2 (A007400 (+ 2 n))))) ;;  Code for A007400 given under that entry. - Antti Karttunen, Aug 12 2017

a(n) = 5 - (A007400(n+2)/2).

A076152 Let c = Sum_{k>=0} 1/2^(k!). Sequence gives values of terms not congruent to 5 in the continued fraction for c.

Original entry on oeis.org

1, 3, 1, 3, 4, 1, 3, 3, 1, 3, 1, 2, 1, 3, 3, 1, 4, 3, 1, 3, 1, 2, 1, 3, 4, 1, 3, 3, 1, 2, 1, 3, 1, 3, 3, 1, 4, 3, 1, 3, 1, 2, 1, 3, 4, 1, 3, 3, 1, 3, 1, 2, 1, 3, 3, 1, 4, 3, 1, 2, 1, 3, 1, 3, 4, 1, 3, 3, 1, 2, 1, 3, 1, 3, 3, 1, 4, 3, 1, 3, 1, 2, 1, 3, 4, 1, 3, 3, 1, 3, 1, 2, 1, 3, 3, 1, 4, 3, 1, 3, 1, 2, 1, 3, 4

Offset: 1

Benoit Cloitre, Nov 02 2002

nonn

Appears to contain only 1,2,3 or 4; seems to be a pseudo-periodic sequence.

			The continued fraction for c is shown in A076157. "Big terms" are all congruent to 5.

Cf. A076154, A076157, A076187.

A076154 Let c = Sum_{k>=0} 1/2^(k!), sequence gives values of terms congruent to 5 of the continued fraction for c.

Original entry on oeis.org

4095, 4722366482869645213695, 4095, 3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121406622895447975679288285306290175, 4095, 4722366482869645213695, 4095

Offset: 1

Benoit Cloitre, Nov 02 2002

nonn

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) ...

			The continued fraction for c is shown in A076157. The "big terms" are all congruent to 5.

Cf. A076152, A076157, A076187.

It seems that for n>=1, a(2n-1)=4095; a(4n-2)=4722366482869645213695 etc.

cp's OEIS Frontend

A092910 a(n) is the (3n+2)-th component of the continued fraction for sum(k>=0,2^(-k!)).

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A076152 Let c = Sum_{k>=0} 1/2^(k!). Sequence gives values of terms not congruent to 5 in the continued fraction for c.

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A076154 Let c = Sum_{k>=0} 1/2^(k!), sequence gives values of terms congruent to 5 of the continued fraction for c.

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Author

Keywords

Comments

Examples

Crossrefs

Formula