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

1,1

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.

Links

Table of n, a(n) for n=1..12.

Example

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.

Prog

(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

Crossrefs

Sequence in context: A083113 A184847 A354743 * A177764 A339402 A027498

Adjacent sequences: A246715 A246716 A246717 * A246719 A246720 A246721

Keyword

base,nonn

Author

James G. Merickel, Nov 15 2014

Extensions

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

Status

approved