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A167764
a(n) is the index k of k-th prime prime(k) in the smallest concatenation "2 3 ... prime(k)" where prime(n+1) is a factor.
3
10, 3, 5, 7, 18, 11, 58, 2, 6, 28, 177, 85, 47, 3, 191, 35, 9, 12, 40, 108, 40, 60, 69, 43, 84, 314, 29, 77, 231, 59, 76, 49, 86, 289, 5, 51, 71, 43, 269, 101, 53, 78, 42, 46, 958, 22, 5, 101, 151, 65, 198, 80, 22, 428, 363, 172, 686, 494, 399, 11, 96, 425, 277, 525
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
Sequence in context: A370632 A224365 A087869 * A241887 A182493 A323763
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