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A243767 Decimal prime numbers which can be split into three equal-sized prime parts whose sum is prime. No leading zeros. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
It appears that the sequence is infinite.
LINKS
EXAMPLE
Prime number 112337 -> 11(prime) + 23(prime) + 37(prime) = 71(prime).
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 *)
PROG
(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
CROSSREFS
Subset of A243766.
Cf. A006879.
Sequence in context: A100607 A092623 A220474 * A345533 A345785 A359449
KEYWORD
nonn,base
AUTHOR
Andreas Boe, Jun 10 2014
STATUS
approved

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)