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A111382 Beginning with 3, least number such that concatenation of first n terms and its digit reversal both are primes.

%I A111382 #16 Jan 03 2025 09:32:33
%S A111382 3,1,1,21,11,43,47,157,753,51,917,273,2409,703,413,3729,1153,6243,
%T A111382 8789,2307,4477,137,403,10649,4617,4533,6133,4721,877,2469,5967,1557,
%U A111382 1047,38931,15533,6877,23987,4767,18049,1463,118333,27897
%N A111382 Beginning with 3, least number such that concatenation of first n terms and its digit reversal both are primes.
%H A111382 Robert Israel, <a href="/A111382/b111382.txt">Table of n, a(n) for n = 1..160</a>
%p A111382 rev:= proc(n) local L,i;
%p A111382   L:= convert(n,base,10);
%p A111382   add(L[-i]*10^(i-1),i=1..nops(L))
%p A111382 end proc;
%p A111382 R:= 3: X:= 3: XR:= 3:
%p A111382 for i from 2 to 50 do
%p A111382   for x from 1 by 2 do
%p A111382     d:= 1+ilog10(x);
%p A111382     t:= X*10^(1+ilog10(x)) + x;
%p A111382     if not isprime(t) then next fi;
%p A111382     xr:= rev(x);
%p A111382     tr:= XR+xr*10^(1+ilog10(XR));
%p A111382     if isprime(tr) then break fi;
%p A111382   od;
%p A111382   X:= t; XR:= tr; R:= R,x;
%p A111382 od:
%p A111382 R; # _Robert Israel_, Aug 09 2023
%o A111382 (Python)
%o A111382 from itertools import count, islice
%o A111382 from gmpy2 import digits, is_prime, mpz
%o A111382 def agen(): # generator of terms
%o A111382     s, r, an = "", "", 3
%o A111382     while True:
%o A111382         yield int(an)
%o A111382         d = digits(an)
%o A111382         s, r, k, sk = s+d, d[::-1]+r, 1, "1"
%o A111382         while not is_prime(mpz(s+sk)) or not is_prime(mpz(sk[::-1]+r)):
%o A111382             k += 2
%o A111382             if k%10 == 5: k += 2
%o A111382             sk = digits(k)
%o A111382         an = k
%o A111382 print(list(islice(agen(), 42))) # _Michael S. Branicky_, Jan 02 2025
%Y A111382 Cf. A113584.
%K A111382 nonn,base
%O A111382 1,1
%A A111382 _Hans Havermann_, Nov 08 2005