A392227 Primes that are the concatenation of x, 1 and x for some x.

313, 919, 17117, 21121, 27127, 29129, 39139, 41141, 47147, 51151, 59159, 71171, 81181, 87187, 89189, 1131113, 1171117, 1191119, 1311131, 1371137, 1411141, 1591159, 1611161, 1771177, 1891189, 2011201, 2391239, 2631263, 2871287, 2911291, 2991299, 3331333, 3591359, 3711371, 3771377, 3891389, 3931393

Offset

1,1

Comments

Primes of the form (10^(d+1)+1) * x + 10^d for some x where 10^(d-1) <= x < 10^d.

Links

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

Example

a(3) = 17117 is a term because it is prime and is the concatenation of 17, 1 and 17.

Maple

R:= NULL:
for d from 1 to 3 do
  for x from 10^(d-1) to 10^d-1 do
    y:= x * (1 + 10^(d+1))+10^d;
    if isprime(y) then
      R:= R, y;
    fi
od od:
R;

Prog

(Python)
from sympy import isprime
from itertools import count, islice
def b(n): return 10**len(str(n))*(10*n+1) + n  # A392225
def agen(): # generator of terms
    yield from (filter(isprime, (b(n) for n in count(1) if n%10 in {1, 3, 7, 9})))
print(list(islice(agen(), 37))) # Michael S. Branicky, Jan 04 2026

Crossrefs

Primes in A392225. Cf. A392226, A392239.

Sequence in context: A090514 A068681 A341802 * A082436 A108845 A348170

Adjacent sequences: A392224 A392225 A392226 * A392228 A392229 A392230

Keyword

nonn,base

Author

Robert Israel, Jan 03 2026

Status

approved