login
Primes from the decimal expansion of Pi, sorted first by the final digit index and then by length.
3

%I #10 Sep 02 2013 02:56:16

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

%T 141592653589,7,97,5897,35897,6535897,5926535897,415926535897,79,

%U 58979,358979,3,589793,2,3,23,9323,9265358979323,2,3,43,643,462643,93238462643,3,433,3,83,383

%N Primes from the decimal expansion of Pi, sorted first by the final digit index and then by length.

%C In this sequence, primes are listed each time they occur (again) with a new ending position, in contrast to A198019 where only the first occurrence of each prime is listed. - _M. F. Hasler_, Sep 02 2013

%e The first digit is 3, which is prime, so a(1) = 3.

%e The second digit is 1, which is no prime, but 31 is prime, so a(2) = 31.

%e The third digit is 4, which does not end any prime.

%e The fourth digit is 1, not prime, but 41 is prime, so a(3) = 41.

%o (PARI) v=[3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3]

%o for(n=1,#v,x=0;p=1;forstep(k=n,1,-1,x+=p*v[k];p*=10;if(v[k]&&isprime(x),print1(x", "))))

%Y Cf. A104841.

%Y Cf. A198018, A198019, A195834, A005042, A047777, A053013, A064467.

%K nonn,base

%O 1,1

%A _Franklin T. Adams-Watters_, Oct 21 2011