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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.

%I A167764 #17 Oct 04 2021 02:07:06
%S A167764 10,3,5,7,18,11,58,2,6,28,177,85,47,3,191,35,9,12,40,108,40,60,69,43,
%T A167764 84,314,29,77,231,59,76,49,86,289,5,51,71,43,269,101,53,78,42,46,958,
%U A167764 22,5,101,151,65,198,80,22,428,363,172,686,494,399,11,96,425,277,525
%N 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.
%C A167764 It is conjectured that this sequence is infinite.
%D A167764 Richard E. Crandall and Carl Pomerance, Prime Numbers, Springer, 2005.
%D A167764 Marcus du Sautoy, Die Musik der Primzahlen: Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen, 2004.
%H A167764 Charles R Greathouse IV, <a href="/A167764/b167764.txt">Table of n, a(n) for n = 1..10000</a>
%e A167764 a(2) = a(14) = 3 because 235 = 5 * 47 = prime(2+1) * prime(14+1) is the concatenation of the first 3 primes.
%e A167764 a(20) = 108 as prime(108) = 593 and the 283-digit concatenation "235...593" has prime factor 73 = prime(20+1).
%o A167764 (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
%o A167764 (Python)
%o A167764 from sympy import nextprime, prime
%o A167764 def a(n):
%o A167764     pn1 = prime(n+1)
%o A167764     k, pk, s = 1, 2, "2"
%o A167764     while int(s)%pn1:
%o A167764         k += 1; pk = nextprime(pk); s += str(pk)
%o A167764     return k
%o A167764 print([a(n) for n in range(1, 65)]) # _Michael S. Branicky_, Oct 03 2021
%K A167764 nonn,base
%O A167764 1,1
%A A167764 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 11 2009, Nov 13 2009
%E A167764 Terms past a(10) and editing by _Charles R Greathouse IV_, Apr 27 2010