cp's OEIS Frontend

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

%I A243767 #20 Dec 06 2022 09:59:11
%S A243767 223,227,337,353,373,557,577,733,757,773,111119,111317,111323,111337,
%T A243767 111347,111373,111731,111773,111779,111913,111953,111959,111973,
%U A243767 111997,112337,112397,112913,112919,112967,112997,113111,113117,113131,113147,113159,113161
%N A243767 Decimal prime numbers which can be split into three equal-sized prime parts whose sum is prime. No leading zeros.
%C A243767 It appears that the sequence is infinite.
%H A243767 Andreas Boe, <a href="/A243767/b243767.txt">Table of n, a(n) for n = 1..10000</a>
%e A243767 Prime number 112337 -> 11(prime) + 23(prime) + 37(prime) = 71(prime).
%t A243767 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 *)
%o A243767 (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
%o A243767 (Python)
%o A243767 from sympy import isprime, primerange
%o A243767 from itertools import count, islice, product
%o A243767 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)))
%o A243767 print(list(islice(agen(), 36))) # _Michael S. Branicky_, Dec 04 2022
%Y A243767 Subset of A243766.
%Y A243767 Cf. A006879.
%K A243767 nonn,base
%O A243767 1,1
%A A243767 _Andreas Boe_, Jun 10 2014