A243766 Decimal numbers which give three prime numbers when split into three equal parts whose sum is prime. No leading zeros.

223, 227, 232, 272, 322, 335, 337, 353, 355, 373, 377, 533, 535, 553, 557, 575, 577, 722, 733, 737, 755, 757, 773, 775, 111119, 111131, 111137, 111161, 111167, 111179, 111313, 111317, 111319, 111323, 111329, 111337, 111343, 111347, 111359, 111373, 111379, 111383

Offset: 1

Author

Andreas Boe, Jun 10 2014

Keywords

• nonn
• base

Comments

It appears that the sequence is infinite.

Examples

			111329 -> 11 + 13 + 29 = 53 = prime.
		

Links

• Andreas Boe, Table of n, a(n) for n = 1..10000

Programs

PARI

first(n) = { my(res = List()); for(i = 1, oo, pow10 = 10^i; pow100 = 100^i; forprime(p = 10^(i-1), 10^i, firstidigs = pow100 * p; forprime(q = 10^(i-1), 10^i, pandq = p+q; first2idigs = firstidigs + pow10*q; forprime(r = 10^(i-1), 10^i, if(isprime(pandq + r), c = first2idigs + r; listput(res, c); if(#res >= n, return(res) ) ) ) ) ) ) } \\ David A. Corneth, Dec 04 2022

Python

from sympy import isprime, primerange
from itertools import count, islice, product
def agen(): yield from (a*10**(2*i) + b*10**i + c for i in count(1) for a, b, c in product(primerange(10**(i-1), 10**i), repeat=3) if isprime(a+b+c))
print(list(islice(agen(), 42))) # Michael S. Branicky, Dec 04 2022