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

1,1

Links

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

Mathematica

Select[Prime[Range[5, 6000]], Part[d=IntegerDigits[#], l=IntegerLength[#]]==Part[d, l-1] && Part[d, 1]==Part[d, 2] &]
(* Alternative: *)
dQ[p_]:=With[{id=IntegerDigits[p]}, Length[Union[Take[id, 2]]]==Length[Union[Take[id, -2]]]==1]; Select[Prime[Range[5, 6000]], dQ] (* Harvey P. Dale, Jul 23 2026 *)

Prog

(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

Crossrefs

Cf. A383978, A384013, A384016.

Subsequence of A050758.

Sequence in context: A267359 A394646 A267940 * A113615 A034873 A075854

Adjacent sequences: A384012 A384013 A384014 * A384016 A384017 A384018

Keyword

nonn,base,changed

Author

Stefano Spezia, May 17 2025

Status

approved