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

Author

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

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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

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