A032625 Primes that are concatenations of n with n + 2.

13, 79, 911, 2729, 3739, 4547, 4951, 5153, 5557, 6163, 6971, 7577, 105107, 109111, 115117, 117119, 121123, 151153, 159161, 181183, 187189, 195197, 201203, 211213, 217219, 225227, 247249, 271273, 277279, 285287, 289291

Offset

1,1

Comments

Or, primes which are the concatenation of two consecutive odd numbers. - Parthasarathy Nambi, Apr 11 2005

There are very few terms with an odd integer length, i.e., which are the concatenation of two consecutive odd primes with different integer lengths. In the first 1000 terms, only 911 and 999910001 have an odd integer length. The next such term is 99999100001. The pattern is fairly obvious. - Harvey P. Dale, May 12 2026

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The first term is 13 which is a prime and is the concatenation of 1 and 3 - the first two odd numbers.

Mathematica

lp = Range[1, 320, 2]; lst = {}; Do[p = FromDigits[ Join[ IntegerDigits[ lp[[n]]], IntegerDigits[ lp[[n + 1]] ]]]; If[ PrimeQ[p], AppendTo[lst, p]], {n, 159}]; lst (* Robert G. Wilson v, Apr 12 2005 *)
Select[#[[1]]*10^IntegerLength[#[[2]]]+#[[2]]&/@Partition[Range[1, 301, 2], 2, 1], PrimeQ] (* Harvey P. Dale, May 12 2026 *)

Crossrefs

Cf. A032607, A032617.

Sequence in context: A125323 A075584 A126481 * A120782 A032652 A236952

Adjacent sequences: A032622 A032623 A032624 * A032626 A032627 A032628

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998

Extensions

Edited by N. J. A. Sloane, May 21 2008 at the suggestion of R. J. Mathar

Status

approved