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A167764 a(n) is index k of k-th prime p(k) in the smallest concatenation "2 3 ... p(k)" where p(n+1) is a factor (n=1,2,3, ...) 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is conjectured that this sequence is infinite.

REFERENCES

Richard E. Crandall, 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 = p(2+1) * p(14+1) is the concatenation of the first 3 primes.

a(20)=108 as p(108)=593 and 283-digit concatenation "235...593" has prime factor 73=p(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)

CROSSREFS

Sequence in context: A010172 A224365 A087869 * A241887 A182493 A323763

Adjacent sequences:  A167761 A167762 A167763 * A167765 A167766 A167767

KEYWORD

nonn,base

AUTHOR

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 11 2009, Nov 13 2009

EXTENSIONS

Program, terms past a(10), and editing by Charles R Greathouse IV, Apr 27 2010

STATUS

approved

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Last modified October 21 11:31 EDT 2019. Contains 328295 sequences. (Running on oeis4.)