A247699 Smallest prime such that, in binary, prefixing and suffixing n-bit numbers, the latter permitted to include leading 0's, does not produce a prime.

3, 5, 523, 47543, 1951071427

Offset: 1

Author

James G. Merickel, Sep 22 2014

Keywords

• nonn
• base
• more
• hard

Examples

			2 in binary, 10, is the middle of the 4-bit prime 1101 (13 in decimal), so a(1) != 2. 3 in binary is 11, and the only number that needs to be checked is binary 1111, the composite 15. So a(1) = 3.
The facts that 63-4=59 and 63-16=47 are primes can be readily seen to rule out 2 and 3 for a(2); so 5 needs to be checked next, looking to see if any of 1010101, 1010111 1110101 or 1110111 may be prime.  The first and last of these are composite by sight, and the others convert to the recognizable composites 87 and 117 in decimal, confirming a(2)=5.
		

Crossrefs

Cf. A172514, A247593.