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Primes occurring in the decimal expansion of Pi (A000796), ordered by position of last digit, then by size.
6

%I #14 Jul 22 2020 11:35:43

%S 3,31,41,5,59,4159,14159,314159,2,53,653,1592653,89,141592653589,7,97,

%T 5897,35897,6535897,5926535897,415926535897,79,58979,358979,589793,23,

%U 9323,9265358979323,43,643,462643,93238462643,433,83,383,2643383,38462643383,89793238462643383,41592653589793238462643383

%N Primes occurring in the decimal expansion of Pi (A000796), ordered by position of last digit, then by size.

%C Cf. A198018; the only difference is that here we list the "new primes" by increasing size (for a given subsequence of A000796).

%C Considering the first 1, 2, 3, 4,.... digits of the decimal expansion 3.14159... of Pi, record the primes that have not occurred earlier.

%C Sequence A198187 lists "duplicate" primes multiple times, each time they occur anew ending in another decimal place. - _M. F. Hasler_, Sep 01 2013

%e In Pi = 3... we have the prime a(1)=3.

%e In Pi = 3.1.... we have the prime a(2)=31.

%e In Pi = 3.14... we have no new prime.

%e In Pi = 3.141.... we have the prime a(3)=41.

%e In Pi = 3.1415.... we have the new prime a(5)=5.

%e In Pi = 3.14159.... we have the new primes (listed in increasing order) a(6)=59, a(7)=4159, a(8)=14159 and a(9)=314159. [_M. F. Hasler_, Sep 01 2013]

%o (PARI) {t=Pi; u=[]; for(i=0,precision(t), for(k=1,i+1, ispseudoprime(p=t\.1^i%10^k)& !setsearch(u,p)& (u=setunion(u,Set(p)))&print1(p",")))}

%Y Cf. A000796, A198018.

%Y Cf. A047777, A053013, A064467.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Oct 20 2011