A088606 - OEIS

%I #27 Jul 16 2021 06:38:50

%S 0,1,0,1,2,1,3,4,2,2,1,1,2,4,3,3,3,4,1,2,1,1,2,3,1,5,1,5,1,2,4,2,2,4,

%T 11,1,4,1,3,6,2,1,3,1,5,6,4,1,5,1,5,2,4,2,3,6,2,3,1,2,1,2,1,2,3,6,3,4,

%U 2,4,6,3,1,1,6,2,2,4,12,1,5,4,5,1,1,5,3,3,3,3,2,5,1,3,1,2,17,2,1,3,3,2,5,5

%N Smallest number k such that concatenation of k and prime(n) is a prime, or 0 if no other number exists. a(1) = a(3) = 0.

%C Subsidiary sequences: (set(1)) Index of the start of the first occurrence of a string of n consecutive 1's or 2's or 3's etc. (set (2)): a(n) = smallest prime such that concatenation of 1 with n successive primes starting from a(n) gives primes in each case. (n primes are obtained.) Similarly for 2, 3, etc. Conjecture: The subsidiary sequences are infinite.

%C A065112(n) = a(n) concatenated with prime(n). - _Bill McEachen_, May 27 2021

%o (PARI) a(n) = if ((n==1) || (n==3), 0, my(k=1); while (!isprime(eval(Str(k, prime(n)))), k++); k); \\ _Michel Marcus_, Jul 11 2021

%Y Cf. A096915, A065112.

%K base,nonn

%O 1,5

%A _Amarnath Murthy_, Oct 15 2003

%E More terms from _Ray Chandler_, Oct 18 2003