A198019 Primes occurring in the decimal expansion of Pi (A000796), ordered by position of last digit, then by size.

3, 31, 41, 5, 59, 4159, 14159, 314159, 2, 53, 653, 1592653, 89, 141592653589, 7, 97, 5897, 35897, 6535897, 5926535897, 415926535897, 79, 58979, 358979, 589793, 23, 9323, 9265358979323, 43, 643, 462643, 93238462643, 433, 83, 383, 2643383, 38462643383, 89793238462643383, 41592653589793238462643383

Offset

1,1

Comments

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

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

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

Links

Table of n, a(n) for n=1..39.

Example

In Pi = 3... we have the prime a(1)=3.
In Pi = 3.1.... we have the prime a(2)=31.
In Pi = 3.14... we have no new prime.
In Pi = 3.141.... we have the prime a(3)=41.
In Pi = 3.1415.... we have the new prime a(5)=5.
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]

Prog

(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", ")))}

Crossrefs

Cf. A000796, A198018.

Cf. A047777, A053013, A064467.

Sequence in context: A045709 A090151 A198187 * A198018 A211003 A068331

Adjacent sequences: A198016 A198017 A198018 * A198020 A198021 A198022

Keyword

nonn,base

Author

M. F. Hasler, Oct 20 2011

Status

approved