A256480 Smallest prime obtained by appending n to a nonzero number with identical digits or 0 if no such prime exists.

0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 211, 0, 113, 0, 0, 0, 317, 0, 419, 0, 421, 0, 223, 0, 0, 0, 127, 0, 229, 0, 131, 0, 233, 0, 0, 0, 137, 0, 139, 0, 241, 0, 443, 0, 0, 0, 347, 0, 149, 0, 151, 0, 353, 0, 0, 0, 157, 0, 359, 0, 461, 0, 163, 0, 0, 0, 167, 0, 269

Offset

0,2

Comments

a(n) = 0 if n is even or a multiple of 5. Conjecture: all other terms are nonzero. Conjecture verified for n <= 10^7.

"Appending" means "on the right".

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv:1503.08883 [math.NT], 2015.

Prog

(Python)
from gmpy2 import digits, mpz, is_prime
def A256480(n, limit=2000):
....sn = str(n)
....if not (n % 2 and n % 5):
........return 0
....for i in range(1, limit+1):
........for j in range(1, 10):
............si = digits(j, 10)*i
............p = mpz(si+sn)
............if is_prime(p):
................return int(p)
....else:
........return 'search limit reached.'

Crossrefs

Cf. A090287, A256481.

Sequence in context: A338827 A055963 A127805 * A088621 A088623 A167166

Adjacent sequences: A256477 A256478 A256479 * A256481 A256482 A256483

Keyword

nonn,base

Author

Chai Wah Wu, Mar 31 2015

Status

approved