OFFSET
1,1
COMMENTS
It is conjectured that this sequence is infinite.
REFERENCES
Richard E. Crandall and Carl Pomerance, Prime Numbers, Springer, 2005.
Marcus du Sautoy, Die Musik der Primzahlen: Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen, 2004.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
a(2) = a(14) = 3 because 235 = 5 * 47 = prime(2+1) * prime(14+1) is the concatenation of the first 3 primes.
a(20) = 108 as prime(108) = 593 and the 283-digit concatenation "235...593" has prime factor 73 = prime(20+1).
PROG
(PARI) a(n)=my(p=prime(n+1), k=2, i=0); forprime(q=3, default(primelimit), i++; if(k%p==0, return(i)); k=k*10^#Str(q)+q) \\ Charles R Greathouse IV, Apr 27 2010
(Python)
from sympy import nextprime, prime
def a(n):
pn1 = prime(n+1)
k, pk, s = 1, 2, "2"
while int(s)%pn1:
k += 1; pk = nextprime(pk); s += str(pk)
return k
print([a(n) for n in range(1, 65)]) # Michael S. Branicky, Oct 03 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 11 2009, Nov 13 2009
EXTENSIONS
Terms past a(10) and editing by Charles R Greathouse IV, Apr 27 2010
STATUS
approved