A104841 The first n-digit prime occurring in the decimal expansion of Pi, A000796.

3, 31, 653, 4159, 14159, 314159, 1592653, 28841971, 795028841, 5926535897, 93238462643, 141592653589, 9265358979323, 23846264338327, 841971693993751, 8628034825342117, 89793238462643383, 348253421170679821, 3832795028841971693, 89793238462643383279

Offset

1,1

Comments

For the next n-digit primes, see the b-file (link).

Sequence A198344 gives the position of these primes withing the digits of Pi.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..1000 (terms 1..162 from M. F. Hasler)

Prog

(PARI) default(realprecision, 2000); A104841(n)={for( c=0, default(realprecision)-n-2, Pi\.1^c%10 & ispseudoprime(p=Pi\.1^(n+c-1)%10^n) & return(p)); error("Please increase default(realprecision) to calculate A104841("n").")}  \\ M. F. Hasler, Oct 23 2011
(Python)
from sympy import S, isprime
pi = "3"+str(S.Pi.n(10**5))[2:] # or load data from file
def A104841_A198344(n): return next(((p, i+1) for i in range(len(pi)-n) if pi[i]!="0" and isprime(p:=int(pi[i:i+n]))), "not enough digits")
print([A104841_A198344(n)[0] for n in range(1, 21)]) # Michael S. Branicky, Dec 28 2022

Crossrefs

Cf. A104819 - A104842.

Cf. A000796, A198344.

Sequence in context: A105293 A377746 A368489 * A092552 A322487 A300735

Adjacent sequences: A104838 A104839 A104840 * A104842 A104843 A104844

Keyword

nonn,base

Author

Zak Seidov, Mar 27 2005

Status

approved