A088606 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.

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, 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, 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

Offset: 1

Author

Amarnath Murthy, Oct 15 2003

Keywords

• base
• nonn

Comments

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.

A065112(n) = a(n) concatenated with prime(n). - Bill McEachen, May 27 2021

Crossrefs

Cf. A096915, A065112.

Programs

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

Extensions

More terms from Ray Chandler, Oct 18 2003