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

11, 19, 41, 61, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, 401, 409, 419, 421, 431, 439, 449, 461, 479, 491, 499, 601, 619, 631, 641, 659, 661, 691, 809, 811, 821, 829, 839, 859, 881, 911, 919, 929, 941, 971, 991, 1009, 1021, 1033, 1039, 1049, 1051

Offset

1,1

Comments

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.

If a number appears in this sequence, it will not appear in A125523, A125524, or A125525.

A000040 is the union of this sequence, A125523, A125524, and A125525.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

479 is prime. The left part of (4)79 is not prime. The right part of 47(9) is not prime.

Maple

q:= n-> isprime(n) and (s-> (h-> not ormap(x-> isprime(parse(x)),
        [s[1..h], s[-h..-1]]))(iquo(length(s), 2)))(""||n):
select(q, [$11..2000])[];  # Alois P. Heinz, Sep 14 2020

Mathematica

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 *)

Prog

(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, ", ")))
(Python)
from sympy import nextprime, isprime
A337508_list, p = [], 11
while p < 10**6:
    s = str(p)
    l = len(s)//2
    if not (isprime(int(s[:l])) or isprime(int(s[-l:]))):
        A337508_list.append(p)
    p = nextprime(p) # Chai Wah Wu, Sep 14 2020

Crossrefs

Cf. A000040, A125523, A125524, A125525.

Sequence in context: A154386 A066738 A278799 * A081027 A322474 A084986

Adjacent sequences: A337505 A337506 A337507 * A337509 A337510 A337511

Keyword

nonn,easy,base

Author

Iain Fox, Aug 30 2020

Status

approved