A382898 Beginning with 13, least prime such that concatenation of first n terms and its digit reversal both are primes.

13, 151, 227, 2083, 887, 79, 2963, 1579, 6287, 1321, 6719, 54919, 26699, 8647, 4229, 3919, 102161, 42433, 1667, 192193, 11633, 186343, 47339, 3259, 65963, 14293, 29717, 61297, 28493, 231367, 43793, 145021, 566441, 475903, 92381, 80473, 139967, 882061, 72893, 709279, 6053, 114487, 1179389, 204331, 203351, 139831, 396239, 205327, 501173, 951589

Offset

1,1

Links

J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..150

Maple

rev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
tcat:= proc(a, b)
  a*10^(1+ilog10(b))+b
end proc:
A:= 13: x:= 13:
for i from 1 to 50 do
   p:= 2:
   do
     p:= nextprime(p);
     y:= tcat(x, p);
     if isprime(y) and isprime(rev(y)) then
          A:= A, p;
          x:= y;
          break
     fi;
   od
od:
A; # after Robert Israel in A113584

Mathematica

w={13}; Do[k=1; q=Monitor[Parallelize[While[True, If[PrimeQ[FromDigits[Join@@IntegerDigits/@Reverse[IntegerDigits[FromDigits[Join@@IntegerDigits/@Append[w, Prime[k]]]]]]]&&PrimeQ[FromDigits[Join@@IntegerDigits/@Append[w, Prime[k]]]], Break[]]; k++]; Prime[k]], {i, k}]; w=Append[w, q], {i, 2, 50}]; w

Prog

(Python)
from itertools import count, islice
from gmpy2 import digits, is_prime, mpz, next_prime
def agen(): # generator of terms
    s, r, an = "", "", 13
    while True:
        yield int(an)
        d = digits(an)
        s, r, p, sp = s+d, d[::-1]+r, 3, "3"
        while not is_prime(mpz(s+sp)) or not is_prime(mpz(sp[::-1]+r)):
            p = next_prime(p)
            sp = digits(p)
        an = p
print(list(islice(agen(), 40))) # after Michael S. Branicky in A113584

Crossrefs

Cf. A113584 (same for 3), A379761 (same for 7), A380227 (same for 11).

Cf. A111382, A111383, A379354, A379355.

Sequence in context: A345217 A185405 A051475 * A242576 A173448 A386359

Adjacent sequences: A382895 A382896 A382897 * A382899 A382900 A382901

Keyword

base,nonn

Author

J.W.L. (Jan) Eerland, Apr 08 2025

Status

approved