A246718 a(n) is the number of different ways of concatenating the numbers {3^k, k=0,...,n} so as to produce a prime number.

2, 2, 3, 44, 128, 619, 4134, 28628, 229132, 2107538, 21438790, 238754555

Offset: 1

Author

James G. Merickel, Nov 15 2014

Keywords

• base
• nonn

Comments

A PARI program distinct from that below was used to compute a(14) using four windows in under a month, but the value was lost.

It is neither trivial nor very difficult to establish that distinct permutations lead to distinct values.

Examples

			The a(1)+a(2)+a(3)+a(4)=51 primes corresponding to the first four terms are, in increasing order, 13, 31, 139, 193, 12739, 19273, 32719, 1273981, 1278139, 1279813, 1381279, 1398127, 1812793, 1819273, 1927813, 2713981, 2718139, 2718193, 2731819, 2738119, 2738191, 2739181, 2781139, 2781193, 2781913, 2793181, 2793811, 2798113, 3127819, 3127981, 3192781, 3271981, 3279811, 3811279, 3812719, 3812791, 3912781, 3918127, 8113279, 8113927, 8119273, 8127319, 8131927, 8139127, 8193127, 9127813, 9181327, 9273181, 9327181, 9812731 and 9813127. Concatenations not shown, such as 931 = 7^2 * 19 and 1392781 = 13 * 107137, are all composite.
		

Programs

PARI

a(n,v=vector(n+1,k,Str(3^(k-1))))=sum(k=1,(n+1)!,ispseudoprime(eval(concat(vecextract(v,numtoperm(n+1,k)))))) \\ M. F. Hasler, Jan 13 2015

Extensions

Edited and verified up to n=9 by M. F. Hasler, Jan 13 2015