A125523 Democratic primes: primes such that the left half of the prime is prime and the right half is not.

29, 31, 59, 71, 79, 211, 229, 239, 241, 251, 269, 271, 281, 311, 331, 349, 359, 379, 389, 509, 521, 541, 569, 571, 599, 701, 709, 719, 739, 751, 761, 769, 1109, 1151, 1163, 1181, 1187, 1193, 1301, 1321, 1327, 1381, 1399, 1709, 1721, 1733, 1777, 1787, 1901

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..50.

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

Example

The left half of 29 is 2, which is prime. The right half is 9, which is not prime.
The left half of 211 is 2, which is prime. The right half is 1, which is not prime.

Prog

(PARI) /* Political primes, democratic case. */ dem(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. A125524, A125525.

Sequence in context: A273547 A132240 A132243 * A156976 A157681 A288615

Adjacent sequences: A125520 A125521 A125522 * A125524 A125525 A125526

Keyword

base,easy,nonn

Author

Cino Hilliard, Jan 22 2007

Status

approved