A256480 - OEIS

%I #14 Apr 19 2015 15:40:28

%S 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,

%T 0,127,0,229,0,131,0,233,0,0,0,137,0,139,0,241,0,443,0,0,0,347,0,149,

%U 0,151,0,353,0,0,0,157,0,359,0,461,0,163,0,0,0,167,0,269

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

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

%C "Appending" means "on the right".

%H Chai Wah Wu, <a href="/A256480/b256480.txt">Table of n, a(n) for n = 0..10000</a>

%H Chai Wah Wu, <a href="http://arxiv.org/abs/1503.08883">On a conjecture regarding primality of numbers constructed from prepending and appending identical digits</a>, arXiv:1503.08883 [math.NT], 2015.

%o (Python)

%o from gmpy2 import digits, mpz, is_prime

%o def A256480(n,limit=2000):

%o ....sn = str(n)

%o ....if not (n % 2 and n % 5):

%o ........return 0

%o ....for i in range(1,limit+1):

%o ........for j in range(1,10):

%o ............si = digits(j,10)*i

%o ............p = mpz(si+sn)

%o ............if is_prime(p):

%o ................return int(p)

%o ....else:

%o ........return 'search limit reached.'

%Y Cf. A090287, A256481.

%K nonn,base

%O 0,2

%A _Chai Wah Wu_, Mar 31 2015