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A249774 The smallest number k such that prime(n)//prime(n+1)//...//prime(n+k-1) is prime, where // is the concatenation function, or 0 if no such k exists. 1

%I

%S 2,0,3,5,3,17,3,29,11,7,2,17,3,19,5,5,7,0,4,14,42,11,2,3,5,5,35,8,

%T 1512,6,36,11,164,4,4,2,2,7,2,2027,23,16,7,0,375,2,9,20,24,3,2,3,57,2,

%U 2,2,186,2,7,16,145,51,3,687,3,3,2,104,23,7,2,3,7,2,34,3,3

%N The smallest number k such that prime(n)//prime(n+1)//...//prime(n+k-1) is prime, where // is the concatenation function, or 0 if no such k exists.

%C a(2) > 4202 or 0, a(18) > 4186 or 0, and a(44) > 4160 or 0.

%F a(n) = A000720(A249775(n)) - n + 1.

%e a(4) starts with prime(4) = 7. 711 is not prime. 71113 is not prime. 7111317 is not prime. 711131719 is prime. Since 711131719 = 7//11//13//17//19, 711131719 is the concatenation of 5 primes, hence a(4) = 5.

%o (PARI) a(n)=s=Str(prime(n));c=0;forprime(p=prime(n)+1,40000,s=concat(s,p); c++;if(ispseudoprime(eval(s)),return(c+1)));0

%o for(n=1,50,print1(a(n),", "))

%Y Cf. A000720, A249775.

%K nonn,base

%O 1,1

%A _Derek Orr_, Nov 05 2014

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)