A256481 Smallest prime obtained by appending a number with identical digits to n or 0 if no such prime exists.

2, 11, 23, 31, 41, 53, 61, 71, 83, 97, 101, 113, 127, 131, 149, 151, 163, 173, 181, 191, 2011, 211, 223, 233, 241, 251, 263, 271, 281, 293, 307, 311, 3299, 331, 347, 353, 367, 373, 383, 397, 401, 419, 421, 431, 443, 457, 461, 479, 487, 491, 503, 511111, 521, 5333

Offset

0,1

Comments

For n <= 15392, a(n) = 0 if and only if n = 6930. Conjecture: if a(n) = 0, then n is divisible by 3. Conjecture verified for n <= 10^6. a(n) = 0 for n = 6930, 50358, 56574, 72975.

Links

Chai Wah Wu, Table of n, a(n) for n = 0..6068

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 mpz, digits, is_prime
def A256481(n, limit=2000):
....if n in (6930, 50358, 56574, 72975):
........return 0
....if n == 0:
........return 2
....sn = str(n)
....for i in range(1, limit+1):
........for j in range(1, 10, 2):
............si = digits(j, 10)*i
............p = mpz(sn+si)
............if is_prime(p):
................return int(p)
....else:
........return 'search limit reached.'

Crossrefs

Cf. A090287, A256480, A030665.

Sequence in context: A106927 A158189 A218255 * A373225 A085745 A106856

Adjacent sequences: A256478 A256479 A256480 * A256482 A256483 A256484

Keyword

nonn,base

Author

Chai Wah Wu, Mar 31 2015

Status

approved