A004200 -id:A004200 - cp's OEIS frontend

A081775 Continued fraction for sum(k>=0,1/7^(2^k-1)).

1, 6, 1, 6, 7, 6, 1, 6, 6, 1, 6, 6, 1, 5, 1, 6, 6, 1, 6, 7, 6, 1, 6, 6, 1, 5, 1, 6, 7, 6, 1, 6, 6, 1, 5, 1, 6, 6, 1, 6, 6, 1, 6, 7, 6, 1, 6, 6, 1, 5, 1, 6, 7, 6, 1, 6, 6, 1, 6, 6, 1, 5, 1, 6, 6, 1, 6, 7, 6, 1, 5, 1, 6, 6, 1, 6, 7, 6, 1, 6, 6, 1, 5, 1, 6, 6, 1, 6, 6, 1, 6, 7, 6, 1, 6, 6, 1, 5, 1, 6, 7, 6, 1, 6, 6

Offset: 1

Benoit Cloitre, Apr 10 2003

Contains only elements 1<=a(n)<=7 ( but 2,3 and 4 never occur)

Cf. A004200.

A081776 Continued fraction for sum(k>=0,1/8^(2^k-1)).

Original entry on oeis.org

1, 7, 1, 7, 8, 7, 1, 7, 7, 1, 7, 7, 1, 6, 1, 7, 7, 1, 7, 8, 7, 1, 7, 7, 1, 6, 1, 7, 8, 7, 1, 7, 7, 1, 6, 1, 7, 7, 1, 7, 7, 1, 7, 8, 7, 1, 7, 7, 1, 6, 1, 7, 8, 7, 1, 7, 7, 1, 7, 7, 1, 6, 1, 7, 7, 1, 7, 8, 7, 1, 6, 1, 7, 7, 1, 7, 8, 7, 1, 7, 7, 1, 6, 1, 7, 7, 1, 7, 7, 1, 7, 8, 7, 1, 7, 7, 1, 6, 1, 7, 8, 7, 1, 7, 7

Offset: 1

Benoit Cloitre, Apr 10 2003

Contains only elements 1<=a(n)<=8 ( but 2,3,4 and 5 never occur)

Cf. A004200.

A081777 Continued fraction for sum(k>=0,1/9^(2^k-1)).

Original entry on oeis.org

1, 8, 1, 8, 9, 8, 1, 8, 8, 1, 8, 8, 1, 7, 1, 8, 8, 1, 8, 9, 8, 1, 8, 8, 1, 7, 1, 8, 9, 8, 1, 8, 8, 1, 7, 1, 8, 8, 1, 8, 8, 1, 8, 9, 8, 1, 8, 8, 1, 7, 1, 8, 9, 8, 1, 8, 8, 1, 8, 8, 1, 7, 1, 8, 8, 1, 8, 9, 8, 1, 7, 1, 8, 8, 1, 8, 9, 8, 1, 8, 8, 1, 7, 1, 8, 8, 1, 8, 8, 1, 8, 9, 8, 1, 8, 8, 1, 7, 1, 8, 9, 8, 1, 8, 8

Offset: 1

Benoit Cloitre, Apr 10 2003

Contains only elements 1<=a(n)<=9 ( but 2,3,4,5 and 6 never occur)

Cf. A004200.

A283874 The Pierce expansion of the number Sum_{k>=1} 1/3^((2^k) - 1).

Original entry on oeis.org

2, 3, 4, 9, 10, 81, 82, 6561, 6562, 43046721, 43046722, 1853020188851841, 1853020188851842, 3433683820292512484657849089281, 3433683820292512484657849089282, 11790184577738583171520872861412518665678211592275841109096961, 11790184577738583171520872861412518665678211592275841109096962

Offset: 0

Kutlwano Loeto, Mar 24 2017

nonn

This sequence is the Pierce expansion of the number 3*s(3) - 1 = 0.370827687432918983346475478500709113969827799141493576... where s(u) = Sum_{k>=0} 1/u^(2^k) for u=3 has been considered by N. J. A. Sloane in A004200.

The continued fraction expansion of the number 3*s(3)-1 is essentially A081771.

			The Pierce expansion of 0.3708276874329189833 starts as 1/2 - 1/(2*3) + 1/(2*3*4) - 1/(2*3*4*9) + 1/(2*3*4*9*10) - 1/(2*3*4*9*10*81) + ...

Jeffrey Shallit, Simple continued fractions for some irrational numbers. J. Number Theory 11 (1979), no. 2, 209-217.

L:=[2]: for k from 0 to 6 do: L:=[op(L),3^(2^k),3^(2^k)+1]: od: print(L);

a(n) = if (n==0, 2, if (n%2, 3^(2^((n-1)/2)), 3^(2^((n-2)/2))+1)); \\ Michel Marcus, Mar 31 2017

a(0) = 2, a(2k+1) = 3^(2^k), a(2k+2) = 3^(2^k) + 1, k >= 0.

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A081775 Continued fraction for sum(k>=0,1/7^(2^k-1)).

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A081776 Continued fraction for sum(k>=0,1/8^(2^k-1)).

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A081777 Continued fraction for sum(k>=0,1/9^(2^k-1)).

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A283874 The Pierce expansion of the number Sum_{k>=1} 1/3^((2^k) - 1).

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