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

1,1

Comments

It appears that the sequence is infinite.

Links

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

Example

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

Prog

(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
(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

Crossrefs

Sequence in context: A163653 A178551 A105982 * A153424 A100607 A092623

Adjacent sequences: A243763 A243764 A243765 * A243767 A243768 A243769

Keyword

nonn,base

Author

Andreas Boe, Jun 10 2014

Status

approved