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A179335
a(n) is the smallest prime which appears as a substring of the decimal representation of prime(n).
4
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
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
KEYWORD
base,nonn
AUTHOR
Reinhard Zumkeller, Jul 11 2010
STATUS
approved