A125524 Republican primes: primes such that the right half of the prime is prime and the left half is not.

13, 17, 43, 47, 67, 83, 97, 103, 107, 113, 127, 137, 157, 163, 167, 173, 193, 197, 433, 443, 457, 463, 467, 487, 607, 613, 617, 643, 647, 653, 673, 677, 683, 823, 827, 853, 857, 863, 877, 883, 887, 907, 937, 947, 953, 967, 977, 983, 997, 1013, 1019, 1031

Offset

2,1

Comments

If the length of n is odd then the central number is not used in the calculation. So neither the left half nor the right half will contain the central digit. If the length of n is even, then all numbers are used.

Links

Table of n, a(n) for n=2..53.

Tony Padilla and Brady Haran, The Most Evil Number, Numberphile video (2018)

Example

The right half of 13 is 3, which is prime. The left half is 1, which is not prime.
The right half of 113 is 3, which is prime. The left half is 1, which is not prime.

Prog

(PARI) /* Political primes, republican case. */ rep(n) = { local(x, ln, y, lp, rp); forprime(x=2, n, y=Str(x); if(x > 9, ln=floor(length(y)/2), ln=1); lp = eval(left(y, ln)); rp = eval(right(y, ln)); if(!isprime(lp)&& isprime(rp), print1(x", ") ) ) }

Crossrefs

Cf. A125523, A125525.

Sequence in context: A279392 A239901 A068497 * A156553 A248474 A140533

Adjacent sequences: A125521 A125522 A125523 * A125525 A125526 A125527

Keyword

base,easy,nonn

Author

Cino Hilliard, Jan 22 2007

Status

approved