A384218 Numbers k such that the concatenations of k and 123456789 in both orders are prime.

217, 409, 629, 653, 779, 871, 881, 1091, 1463, 1489, 1913, 1993, 2039, 2729, 2881, 3397, 3649, 3677, 3751, 3961, 4073, 4321, 4843, 4961, 5039, 5507, 5609, 5683, 5849, 5941, 6593, 6613, 6713, 6923, 7349, 7571, 7789, 7907, 8413, 8419, 8617, 8623, 8687, 8689, 8797, 8909, 9083, 9589, 9973, 10241

Offset

1,1

Comments

Numbers k such that both concatenations k123456789 and 123456789k are prime.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 629 is a term because 629123456789 and 123456789629 are prime.

Maple

filter:= proc(n) isprime(n*10^9+123456789) and
 isprime(123456789*10^(1+ilog10(n))+n) end proc;
select(filter, [seq(i, i=1..20000, 2)]);

Mathematica

Select[Range[1, 12000, 2], PrimeQ[#*10^9 + 123456789] && PrimeQ[123456789*10^IntegerLength[#] + #] &] (* Paolo Xausa, May 23 2025 *)

Prog

(Python)
from sympy import isprime
def ok(n): s = str(n); return all(isprime(int(t)) for t in ["123456789"+s, s+"123456789"])
print([k for k in range(10**4) if ok(k)]) # Michael S. Branicky, May 22 2025

Crossrefs

Intersection of A232725 and A232727.

Cf. A384174.

Sequence in context: A102658 A145732 A038594 * A020232 A019422 A231558

Adjacent sequences: A384215 A384216 A384217 * A384219 A384220 A384221

Keyword

nonn,base

Author

Robert Israel, May 22 2025

Status

approved