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A109374 Irregular table read by rows: Row n is the terms of the continued fraction for prime(n+1)/prime(n). 6

%I #21 Oct 13 2019 09:44:26

%S 1,2,1,1,2,1,2,2,1,1,1,3,1,5,2,1,3,4,1,8,2,1,4,1,3,1,3,1,5,1,14,2,1,5,

%T 6,1,9,4,1,20,2,1,10,1,3,1,7,1,5,1,8,1,5,1,29,2,1,10,6,1,16,1,3,1,35,

%U 2,1,12,6,1,19,1,3,1,13,1,5,1,11,8,1,24,4,1,50,2,1,25,1,3,1,53,2,1,27,4,1

%N Irregular table read by rows: Row n is the terms of the continued fraction for prime(n+1)/prime(n).

%C Sequence A071866 gives the number of terms in the n-th continued fraction.

%C If n is in A029707, row n is [1, (prime(n)-1)/2, 2]. - _Robert Israel_, May 29 2018

%H Robert Israel, <a href="/A109374/b109374.txt">Table of n, a(n) for n = 1..10003</a> (rows 1 to 2533, flattened)

%e Prime(4)/prime(3) = 7/5 = 1+ 1/(2+1/2), so the terms associated with the 3rd continued fraction are 1, 2, 2.

%p seq(op(convert(ithprime(n+1)/ithprime(n), confrac)),n=1..100); # _Robert Israel_, May 29 2018

%t Flatten[Table[ContinuedFraction[Prime[n + 1]/Prime[n]], {n, 30}]] (* _Ray Chandler_, Aug 25 2005 *)

%Y Cf. A029707, A071866, A110021, A112323, A112324, A112768.

%K nonn,tabf,look

%O 1,2

%A _Leroy Quet_, Aug 24 2005

%E Extended by _Ray Chandler_ and _Robert G. Wilson v_, Aug 25 2005

%E Edited by _Charles R Greathouse IV_, Apr 23 2010

%E Definition corrected by _Leroy Quet_, May 10 2010

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Last modified April 25 09:33 EDT 2024. Contains 371967 sequences. (Running on oeis4.)