A379782 -id:A379782 - cp's OEIS frontend

A379355 Beginning with 3, least prime such that the reversal concatenation of first n terms is prime.

3, 2, 2, 13, 2, 13, 59, 31, 263, 73, 23, 31, 449, 31, 59, 313, 2, 3, 211, 317, 31, 449, 241, 887, 349, 911, 853, 887, 313, 173, 1777, 179, 967, 503, 331, 113, 163, 359, 1153, 281, 97, 1823, 13, 23, 1657, 269, 223, 3623, 2017, 233, 61, 1361, 367, 1031, 79, 389, 577, 2963, 1741, 59, 13, 1439, 463, 797

Offset: 1

J.W.L. (Jan) Eerland, Dec 21 2024

"Reverse concatenation" here seems to refer 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". - N. J. A. Sloane, Jan 03 2025

Michael S. Branicky, Table of n, a(n) for n = 1..1000

Cf. A111382, A111383, A113584, A379354.

The primes produced are in A379782.

w = {3};
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, 57}];
w

from itertools import count, islice
from gmpy2 import digits, is_prime, mpz, next_prime
def agen(): # generator of terms
    r, an = "", 3
    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(), 57))) # Michael S. Branicky, Dec 21 2024

A202997 a(1) = 3 ; a(n+1) is the prime number obtained by the concatenation {p, a(n)} where p is the smallest prime prefix.

Original entry on oeis.org

3, 23, 223, 31223, 231223, 31231223, 2931231223, 372931231223, 17372931231223, 1317372931231223, 1971317372931231223, 1571971317372931231223, 891571971317372931231223, 79891571971317372931231223, 25179891571971317372931231223, 4325179891571971317372931231223

Offset: 1

Michel Lagneau, Dec 27 2011

By Xylouris' version of Linnik's theorem, a(n) << 3^(6.2^n + cn) for some constant c. [Charles R Greathouse IV, Dec 27 2011]

			a(1) = 3;
a(2) = 23 because 2 is the smallest prime prefix and 23 is prime;
a(3) = 223 because 2 is the smallest prime prefix and 223 is prime;
a(4) = 31223 because 31 is the smallest prime prefix and 31223 is prime.

Cf. A173291, A379354, A379355, A379782.

a0:=3: printf(`%d, `,a0):for it from 1 to 20 do: i:=0:for n from 1 to 1000 while(i=0)  do:p0:=ithprime(n):n0:=length(a0):x:=p0*10^n0+a0: if type(x,prime)=true then printf(`%d, `,x):i:=1:a0:=x:else fi:od:od:

cp's OEIS Frontend

A379355 Beginning with 3, least prime such that the reversal concatenation of first n terms is prime.

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