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A128850 Numerator of the continued fraction convergents of the decimal concatenation of prime-indexed primes. 0

%I

%S 0,1,1,6,7,13,33,46,79,204,283,487,770,1257,22139,23396,45535,68931,

%T 183397,252328,940381,3073471,7087323,24335440,153099963,330535366,

%U 3458453623,3788988989,7247442612,11036431601,29320305814,274919183927

%N Numerator of the continued fraction convergents of the decimal concatenation of prime-indexed primes.

%C Pips of order 1, pips(1) = prime(prime(x)). Pips of order 2, pips(2) = prime(prime(prime(x))) etc.

%F Prime-indexed primes (pips)or primeth primes 3, 5, 11, 17, 31, 41, 59, 67, ... are concatenated and then preceded by a decimal point to create the fraction N = .35111731415967... 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.

%o (PARI) cattpips(n) = { a=".";forprime(x=2,n,a=concat(a,prime(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","); ) }

%K frac,nonn,base

%O 0,4

%A _Cino Hilliard_, Apr 16 2007

%E Edited by _Charles R Greathouse IV_, Apr 25 2010

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)