A243767 Decimal prime numbers which can be split into three equal-sized prime parts whose sum is prime. No leading zeros.

223, 227, 337, 353, 373, 557, 577, 733, 757, 773, 111119, 111317, 111323, 111337, 111347, 111373, 111731, 111773, 111779, 111913, 111953, 111959, 111973, 111997, 112337, 112397, 112913, 112919, 112967, 112997, 113111, 113117, 113131, 113147, 113159, 113161

Offset: 1

Author

Andreas Boe, Jun 10 2014

Keywords

• nonn
• base

Comments

It appears that the sequence is infinite.

Examples

			Prime number 112337 -> 11(prime) + 23(prime) + 37(prime) = 71(prime).
		

Links

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

Crossrefs

Subset of A243766.

Cf. A006879.

Programs

Mathematica

Join[Select[FromDigits/@Select[Tuples[Prime[Range[4]],3],PrimeQ[Total[ #]]&],PrimeQ],Select[ FromDigits[Flatten[IntegerDigits/@#]]&/@Select[ Tuples[ Prime[Range[5,25]],3],PrimeQ[Total[#]]&],PrimeQ]] (* The program generates the first 1283 terms of the sequence, i.e., all terms with six digits or less. *) (* Harvey P. Dale, Dec 04 2022 *)

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; if(isprime(c), 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 filter(isprime, (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(), 36))) # Michael S. Branicky, Dec 04 2022