A179335 a(n) is the smallest prime which appears as a substring of the decimal representation of prime(n).

2, 3, 5, 7, 11, 3, 7, 19, 2, 2, 3, 3, 41, 3, 7, 3, 5, 61, 7, 7, 3, 7, 3, 89, 7, 101, 3, 7, 109, 3, 2, 3, 3, 3, 149, 5, 5, 3, 7, 3, 7, 181, 19, 3, 7, 19, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 401, 409, 19, 2, 3, 3, 3, 3, 449, 5, 61, 3, 7, 7, 7

Offset

1,1

Comments

a(n) < 10 iff prime(n) is in A179336;

a(n) = prime(n) iff prime(n) is in A033274. [Corrected by M. F. Hasler, Aug 27 2012]

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Prog

(PARI) A179335(n)={my(p=prime(n), m=0, M); for(d=1, n, M=10^d; n=p; until(n<=M || !n\=10, isprime(n%M) & (!m || m>n%M) & m=n%M); m & return(m))} \\ M. F. Hasler, Aug 27 2012
(Python)
from sympy import isprime, prime
def a(n):
    s = str(prime(n))
    ss = set(int(s[i:i+1+l]) for i in range(len(s)) for l in range(len(s)))
    return min(t for t in ss if isprime(t))
print([a(n) for n in range(1, 94)]) # Michael S. Branicky, Jun 29 2022

Crossrefs

Cf. A000040, A070024, A019546, A092629, A104250, A019546, A034844, A179336, A193238.

Sequence in context: A194262 A039710 A087173 * A330994 A097858 A084408

Adjacent sequences: A179332 A179333 A179334 * A179336 A179337 A179338

Keyword

base,nonn

Author

Reinhard Zumkeller, Jul 11 2010

Status

approved