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Search: id:A128850
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| A128850 |
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Numerator of the continued fraction convergents of the decimal concatenation of prime-index-primes. |
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+0
1
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| 0, 1, 1, 6, 7, 13, 33, 46, 79, 204, 283, 487, 770, 1257, 22139, 23396, 45535, 68931, 183397, 252328, 940381, 3073471, 7087323, 24335440, 153099963, 330535366, 3458453623, 3788988989, 7247442612, 11036431601, 29320305814, 274919183927
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Pips of order 1, pips(1) = prime(prime(x)). Pips of order 2, pips(2) = prime(prime(prime(x))) etc.
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FORMULA
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Prime-index-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
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PROGRAM
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(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", "); ) }
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CROSSREFS
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Adjacent sequences: A128847 A128848 A128849 this_sequence A128851 A128852 A128853
Sequence in context: A042723 A020689 A128844 this_sequence A042025 A041072 A041999
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KEYWORD
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frac,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Apr 16 2007
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