A111383 Beginning with 3, least member of A007500 such that concatenation of first n terms and its digit reversal both are primes.

3, 7, 3, 3, 79, 701, 157, 1103, 11959, 1901, 10273, 92753, 17047, 11909, 144973, 327251, 99289, 92831, 90373, 309671, 1149619, 745397, 1232083, 94793, 18481, 76607, 186649, 181421, 1657561, 3746111, 7067239, 324143, 3185263, 9457181, 1703413, 3517583, 72481, 12859481

Offset: 1

Author

Hans Havermann, Nov 08 2005

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..164

Crossrefs

Cf. A113584, A111382, A007500.

Programs

Python

from gmpy2 import digits, is_prime, mpz
from itertools import count, islice, product
def bgen(): # generator of terms of A007500 -{2, 5} as strings
    yield from "37"
    p = 11
    for digits in count(2):
        for first in "1379":
            for mid in product("0123456789", repeat=digits-2):
                for last in "1379":
                    s = first + "".join(mid) + last
                    if is_prime(mpz(s)) and is_prime(mpz(s[::-1])):
                        yield s
def agen(): # generator of terms
    s, r, an, san = "", "", 3, "3"
    while True:
        yield int(an)
        s, r = s+san, san[::-1]+r
        for san in bgen():
            if is_prime(mpz(s+san)) and is_prime(mpz(san[::-1]+r)):
                break
        an = mpz(san)
print(list(islice(agen(), 34))) # Michael S. Branicky, Jan 02 2025

Extensions

a(35) and beyond from Michael S. Branicky, Jan 02 2025