cp's OEIS Frontend

A337508 Primes such that neither the left half nor the right half of the prime is prime.

%I A337508 #19 Aug 09 2023 16:18:42
%S A337508 11,19,41,61,89,101,109,131,139,149,151,179,181,191,199,401,409,419,
%T A337508 421,431,439,449,461,479,491,499,601,619,631,641,659,661,691,809,811,
%U A337508 821,829,839,859,881,911,919,929,941,971,991,1009,1021,1033,1039,1049,1051
%N A337508 Primes such that neither the left half nor the right half of the prime is prime.
%C A337508 For n > 9, the center digit is not considered when making the calculation. For a prime number to be in this sequence, both the substring to the left of the center and the substring to the right of the center must be nonprime.
%C A337508 If a number appears in this sequence, it will not appear in A125523, A125524, or A125525.
%C A337508 A000040 is the union of this sequence, A125523, A125524, and A125525.
%H A337508 Harvey P. Dale, <a href="/A337508/b337508.txt">Table of n, a(n) for n = 1..1000</a>
%e A337508 479 is prime. The left part of (4)79 is not prime. The right part of 47(9) is not prime.
%p A337508 q:= n-> isprime(n) and (s-> (h-> not ormap(x-> isprime(parse(x)),
%p A337508         [s[1..h], s[-h..-1]]))(iquo(length(s), 2)))(""||n):
%p A337508 select(q, [$11..2000])[];  # _Alois P. Heinz_, Sep 14 2020
%t A337508 lhrhQ[p_]:=Module[{idp=IntegerDigits[p],c},c=Floor[Length[idp]/2];AllTrue[ {FromDigits[ Take[idp,c]],FromDigits[Take[idp,-c]]},!PrimeQ[#]&]]; Select[Prime[Range[5,200]],lhrhQ] (* _Harvey P. Dale_, Aug 09 2023 *)
%o A337508 (PARI) lista(nn) = forprime(p=11, nn, my(l=#Str(p), e=floor(l/2), left=floor(p/10^(e+l%2)), right=p-floor(p/10^e)*10^e); if(!isprime(left) && !isprime(right), print1(p, ", ")))
%o A337508 (Python)
%o A337508 from sympy import nextprime, isprime
%o A337508 A337508_list, p = [], 11
%o A337508 while p < 10**6:
%o A337508     s = str(p)
%o A337508     l = len(s)//2
%o A337508     if not (isprime(int(s[:l])) or isprime(int(s[-l:]))):
%o A337508         A337508_list.append(p)
%o A337508     p = nextprime(p) # _Chai Wah Wu_, Sep 14 2020
%Y A337508 Cf. A000040, A125523, A125524, A125525.
%K A337508 nonn,easy,base
%O A337508 1,1
%A A337508 _Iain Fox_, Aug 30 2020