A128844 Numerators of the continued fraction convergents of the decimal concatenation of the lower bound of twin primes.

0, 1, 1, 6, 7, 13, 33, 46, 79, 204, 283, 487, 770, 1257, 3284, 4541, 7825, 12366, 20191, 517141, 537332, 17711765, 35960862, 89633489, 10702346053, 53601363754, 439513256085, 493114619839, 932627875924, 2358370371687, 3290998247611

Offset

0,4

Links

Table of n, a(n) for n=0..30.

Formula

The lower bounds of twin primes 3,5,11,17... are concatenated and then preceded by a decimal point to create the fraction N = .35111729... . This number is then evaluated with n=0,m=steps to iterate,x = N, a(0)=floor(N) using the loop: do a(n)=floor(x) x=1/(x-a(n)) n=n+1 loop until n=m

Prog

(PARI) cattwinsL(n) = a="."; forprime(x=3, n, if(ispseudoprime(x+2), a=concat(a, Str(x)))); a=eval(a) cfrac2(m, f) = { default(realprecision, 1000); cf = vector(m+10); cf = contfrac(f); for(m1=1, m-1, r=cf[m1+1]; forstep(n=m1, 1, -1, r = 1/r; r+=cf[n]; ); numer=numerator(r); denom=denominator(r); print1(numer", "); ) }

Crossrefs

Sequence in context: A042723 A160825 A020689 * A128850 A042025 A041072

Adjacent sequences: A128841 A128842 A128843 * A128845 A128846 A128847

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 16 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved