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Decimal numbers which give three prime numbers when split into three equal parts whose sum is prime. No leading zeros.
2

%I #19 Dec 06 2022 09:26:31

%S 223,227,232,272,322,335,337,353,355,373,377,533,535,553,557,575,577,

%T 722,733,737,755,757,773,775,111119,111131,111137,111161,111167,

%U 111179,111313,111317,111319,111323,111329,111337,111343,111347,111359,111373,111379,111383

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

%C It appears that the sequence is infinite.

%H Andreas Boe, <a href="/A243766/b243766.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (Python)

%o from sympy import isprime, primerange

%o from itertools import count, islice, product

%o 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))

%o print(list(islice(agen(), 42))) # _Michael S. Branicky_, Dec 04 2022

%o (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

%K nonn,base

%O 1,1

%A _Andreas Boe_, Jun 10 2014