A100552 Single-digit primes, followed recursively by 2k-digit primes obtained by concatenation of pairs of distinct k-digit primes of the sequence.

2, 3, 5, 7, 23, 37, 53, 73, 5323

Offset

1,1

Comments

The sequence is finite because there is only one 4-digit prime from which no further 8-digit primes can be obtained as there are no 4-digit partners left.

Links

Table of n, a(n) for n=1..9.

Example

Start from the 4 single-digit primes 2,3,5,7. Construct all 2-digit primes with prime digits (to get the first 8 elements of A019546). Add the 4-digit primes obtained by concatenation of the previous 2-digit primes.

Mathematica

a={2, 3, 5, 7} (* two digits primes*) b=Delete[Union[Flatten[Table[If[PrimeQ[a[[n]]*10+a[[m]]]==True, a[[n]]*10+a[[m]], 0], {n, 1, 4}, {m, 1, 4}], 1]], 1] (* only one four digit prime combination exists*) c=Delete[Union[Flatten[Table[If[PrimeQ[b[[n]]*100+b[[m]]]==True, b[[n]]*100+b[[m]], 0], {n, 1, 4}, {m, 1, 4}], 1]], 1] (* no eight digit prime of this type exists*) d=If[PrimeQ[c[[1]]*10000+c[[1]]]==True, c[[1]]*100+c[[1]], 0] Join[a, b, c]

Crossrefs

Sequence in context: A085823 A284060 A211682 * A210566 A155873 A362678

Adjacent sequences: A100549 A100550 A100551 * A100553 A100554 A100555

Keyword

nonn,base,fini,full,less

Author

Roger L. Bagula, Nov 27 2004

Extensions

Edited by the associate editors of the OEIS, Jun 28 2009

Status

approved