A384015 Primes with at least two identical trailing digits and at least two identical leading digits.

11, 11177, 11299, 11311, 11399, 11411, 11633, 11677, 11699, 11777, 11833, 11933, 22111, 22133, 22277, 22433, 22511, 22699, 22777, 22811, 22877, 33199, 33211, 33311, 33377, 33533, 33577, 33599, 33811, 33911, 44111, 44533, 44633, 44699, 44711, 44777, 55333, 55399

Offset: 1

Author

Stefano Spezia, May 17 2025

Keywords

• nonn
• base

Crossrefs

Cf. A383978, A384013, A384016.

Subsequence of A050758.

Programs

Mathematica

Select[Prime[Range[5,6000]],Part[d=IntegerDigits[#],l=IntegerLength[#]]==Part[d,l-1] && Part[d,1]==Part[d,2] &]

Python

from itertools import count, islice
from sympy import isprime
def A384015_gen(): # generator of terms
    yield 11
    for n in count(2):
        yield from filter(isprime,(i+j+k for i in range(11*10**(n-2),11*10**(n-1),11*10**(n-2)) for j in range(0,10**(n-2),100) for k in (11,33,77,99)))
A384015_list = list(islice(A384015_gen(),38)) # Chai Wah Wu, May 20 2025