A379761 Beginning with 7, least prime such that concatenation of first n terms and its digit reversal both are primes.

7, 3, 3, 31, 389, 1021, 2243, 1831, 5849, 15361, 9887, 3877, 4157, 919, 22637, 14449, 27617, 80221, 5039, 51043, 14009, 126079, 24443, 68311, 49193, 47059, 13049, 253681, 271409, 221227, 138869, 116953, 146297, 21841, 1211549, 322501, 212633, 281791, 216071, 1901749, 38747, 116437

Offset

1,1

Links

J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..100

Example

31 is a term because the concatenation of {7,3,3,31} and {13,3,3,7} are respectively 73331 and 13337 which are both prime.
2243 is a term because the concatenation of {7,3,3,31,389,1021,2243} and {3422,1201,983,13,3,3,7} are respectively 7333138910212243 and 3422120198313337 which are both prime.

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:= 7: x:= 7:
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={7}; 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 = "", "", 7
    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))) # Michael S. Branicky, Jan 02 2025

Crossrefs

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

Sequence in context: A169813 A380011 A097517 * A127559 A066747 A240908

Adjacent sequences: A379758 A379759 A379760 * A379762 A379763 A379764

Keyword

base,nonn,changed

Author

J.W.L. (Jan) Eerland, Jan 02 2025

Status

approved