A380011 Beginning with 7, least prime such that the reversal concatenation of the first n terms is prime.

7, 3, 3, 13, 3, 2, 13, 47, 43, 47, 37, 41, 109, 41, 139, 149, 109, 263, 73, 563, 163, 41, 19, 797, 61, 107, 31, 821, 43, 149, 37, 953, 211, 89, 547, 353, 337, 167, 67, 239, 1009, 449, 97, 23, 349, 41, 31, 911, 61, 929, 229, 797, 331, 191, 463, 107, 463, 809, 2887, 971

Offset: 1

Author

J.W.L. (Jan) Eerland, Jan 09 2025

Keywords

• base
• nonn

Comments

"Reverse concatenation" here refers to the decimal concatenation R(a(n)) || R(a(n-1)) || ... || R(a(3)) || R(a(2)) || R(a(1)) where R(k) means "reverse digits of k".

Links

• J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..982

Crossrefs

Cf. A111382, A111383, A113584, A379354, A379355, A379761, A380010.

Programs

Mathematica

w={7};Do[k=1;q=Monitor[Parallelize[While[True,If[PrimeQ[FromDigits[Join@@IntegerDigits/@Reverse[IntegerDigits[FromDigits[Join@@IntegerDigits/@Append[w,Prime[k]]]]]]],Break[]];k++];Prime[k]],k];w=Append[w,q],{i,2,50}];w

Python

from itertools import count, islice
from gmpy2 import digits, is_prime, mpz, next_prime
def agen(): # generator of terms
    r, an = "", 7
    while True:
        yield int(an)
        r = digits(an)[::-1] + r
        p = 2
        while not is_prime(mpz(digits(p)[::-1]+r)): p = next_prime(p)
        an = p
print(list(islice(agen(), 50))) # after Michael S. Branicky in A379355