A052089 Primes formed by concatenating k with k-1.

43, 109, 2221, 2423, 3433, 4241, 5857, 7069, 7877, 8887, 10099, 102101, 108107, 112111, 114113, 124123, 148147, 154153, 160159, 172171, 180179, 192191, 198197, 202201, 208207, 210209, 214213, 238237, 244243, 262261, 264263, 268267, 270269, 282281, 294293, 300299

Offset: 1

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base
• changed

Examples

			2423 is a prime and a concatenation of 24 and 23.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A030458, A052087, A052088.

Programs

Magma

[Seqint(Intseq(n-1) cat Intseq(n)): n in [2..300 by 2] | IsPrime(Seqint(Intseq(n-1) cat Intseq(n)))]; // Marius A. Burtea, Mar 21 2019

Mathematica

Sort[Select[FromDigits[Flatten[IntegerDigits/@#]]&/@Partition[ Range[ 300,1,-1],2,1],PrimeQ]] (* Harvey P. Dale, May 09 2012 *)
Select[Table[n 10^IntegerLength[n-1]+n-1,{n,2,300}],PrimeQ] (* Harvey P. Dale, Aug 20 2025 *)

PARI

for(n=4,1e4,if(isprime(t=eval(Str(n,n-1))),print1(t", "))) \\ Charles R Greathouse IV, May 07 2013

Python

from sympy import isprime
from itertools import count, islice
def agen(): yield from filter(isprime, (int(str(k)+str(k-1)) for k in count(2, 2)))
print(list(islice(agen(), 36))) # Michael S. Branicky, Aug 05 2022