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Indices for which A001203 (continued fraction for Pi) is prime.
4

%I #7 Aug 07 2019 13:25:48

%S 1,2,9,11,14,17,18,19,20,23,27,28,31,36,37,39,40,46,48,49,50,52,59,65,

%T 70,71,72,73,75,85,86,90,93,95,97,101,102,105,106,109,110,111,118,120,

%U 122,123,124,127,128,131,132,133,140,142,145,146,151,152,153,155,159

%N Indices for which A001203 (continued fraction for Pi) is prime.

%F k is in A138759 <=> A001203(k) is in A000040

%e This sequence starts 1,2,9,11,... since the first, 2nd, 9th, 11th...

%e term of sequence A001203 = (3, 7, 15, 1, 292, 1, 1, 1, 2, ...) are primes.

%t Position[ContinuedFraction[Pi,200],_?PrimeQ]//Flatten(* _Harvey P. Dale_, Aug 07 2019 *)

%o (PARI) default(realprecision,1000); t=contfrac(Pi); for( k=1,#t, isprime(t[k]) & print1(k","))

%Y Cf. A001203, A005042, A107892, A138758.

%K nonn

%O 1,2

%A _M. F. Hasler_, Mar 31 2008