A138759 -id:A138759 - cp's OEIS frontend

A032523 Index of first occurrence of n as a term in A001203, the continued fraction for Pi.

4, 9, 1, 30, 40, 32, 2, 44, 130, 100, 276, 55, 28, 13, 3, 78, 647, 137, 140, 180, 214, 83, 203, 91, 791, 112, 574, 175, 243, 147, 878, 455, 531, 421, 1008, 594, 784, 3041, 721, 1872, 754, 119, 492, 429, 81, 3200, 825, 283, 3027, 465, 1437, 3384, 1547, 1864, 446

Offset: 1

Wouter Meeussen

Incorrectly indexed version of A225802 (assuming the c.f. is [a_1; a_2, a_3, ...] instead of [a_0; a_1, a_2, ...]).
Until it is proved that every integer n>0 does occur in A001203, we should tacitly understand a convention like "A032523(n) = 0 if n does not occur in A001203". - M. F. Hasler, Mar 31 2008
All positive integers <= 33674 occur in the first 5,821,569,425 terms of the c.f. - Eric W. Weisstein, Sep 19 2011
All positive integers <= 47086 occur in the first 10,672,905,501 terms of the c.f. (the first that do not are 47087, 49004, 50465, 50471, ...) - Eric W. Weisstein, Jul 18 2013

M. F. Hasler and Eric W. Weisstein, Table of n, a(n) for n = 1..47086 (terms n = 1..3131 from _M. F. Hasler_, using data from H. Havermann)
H. Havermann, 24345 terms of a trivial variation (first term of Pi excluded) of A032523
Eric Weisstein's World of Mathematics, Pi Continued Fraction

Cf. A225802 (= a(n) - 1).

Cf. A001203, A107892, A138758, A138759.

With[{cfp=ContinuedFraction[Pi,5000]},Flatten[Table[Position[cfp,n,1,1],{n,60}]]] (* Harvey P. Dale, Dec 11 2012 *)

default( realprecision, 15000); v=contfrac(Pi); a(n) = for( i=1,#v, v[i]==n && return(i)) \\ - W. Meeussen, simplified by M. F. Hasler, Mar 31 2008

a(n) = A225802(n) + 1.

A032523(n) = min { k | A001203(k)=n }. - M. F. Hasler, Mar 31 2008

Edited by M. F. Hasler, Mar 31 2008

A107892 Index of first occurrence of n-th prime in A001203, the continued fraction for Pi.

Original entry on oeis.org

9, 1, 40, 2, 276, 28, 647, 140, 203, 243, 878, 784, 754, 492, 825, 1547, 907, 868, 1789, 9215, 898, 6222, 9131, 4829, 1516, 6700, 22640, 872, 11170, 3204, 223, 10387, 8299, 30086, 31079, 12637, 8486, 20644, 8451, 53069, 32093, 16297, 20276, 1002, 21264

Offset: 1

Zak Seidov, May 25 2005

nonn

Until it is proved that every prime does indeed occur in A001203, we should tacitly understand a convention like "A107892(n) = 0 if A000040(n) does not occur in A001203". - M. F. Hasler, Mar 31 2008

Among first 1000000 terms of the continued fraction for Pi, the first absent primes have indices 129, 132, 137, 146, 147, 158, 160, 165, 170, 172, 175, 180, 182, 184, 189, 193, 197, 198, 199. The 200th prime is in the 947040th place, thus A107892(200)=947040.

M. F. Hasler (using data from H. Havermann), Table of n, a(n) for n=1,...,445.

Cf. A032523: first occurrence of n in A001203.

Cf. A138758, A138759.

A107892(n) = A032523(A000040(n)) = min { k | A001203(k)=A000040(n) }. - M. F. Hasler, Mar 31 2008

Edited by M. F. Hasler, Mar 31 2008

A138758 Index of A001203(n) (continued fraction for Pi) in A000040 (primes), or 0 if A001203(n) is not prime.

Original entry on oeis.org

2, 4, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 6, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 3, 0, 0, 0, 0, 0, 4, 0, 1, 2, 4, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 3, 0, 0, 1

Offset: 1

M. F. Hasler, Mar 31 2008

nonn

			This sequence starts 2,4,0,0,... since the 1st and 2nd terms of the continued fraction expansion of Pi, A001203 = (3, 7, 15, 1, ...) are the 2nd resp. 4th primes, while the next two terms are not primes.

Cf. A001203, A138757, A138759, A005042.

default(realprecision,1000); t=contfrac(Pi); vector(#t,i,isprime(t[i])*primepi(t[i]))

a(n) = A000720(A001203(n)) * A010051(A001203(n)).

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A032523 Index of first occurrence of n as a term in A001203, the continued fraction for Pi.

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A107892 Index of first occurrence of n-th prime in A001203, the continued fraction for Pi.

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A138758 Index of A001203(n) (continued fraction for Pi) in A000040 (primes), or 0 if A001203(n) is not prime.

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