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A385968 Triprimes that are concatenations of three consecutive primes, and whose prime factors sum to a prime.

%I A385968 #10 Jul 21 2025 21:43:30
%S A385968 199211223,331337347,367373379,487491499,653659661,859863877,
%T A385968 102110311033,106910871091,111711231129,112911511153,130313071319,
%U A385968 143914471451,165716631667,178918011811,214321532161,226722692273,246724732477,274127492753,274927532767,284328512857,330133073313,362336313637
%N A385968 Triprimes that are concatenations of three consecutive primes, and whose prime factors sum to a prime.
%H A385968 Robert Israel, <a href="/A385968/b385968.txt">Table of n, a(n) for n = 1..10000</a>
%e A385968 a(3) = 367373379 is a term because it is the concatenation of consecutive primes 367, 373 and 379 and is the product of three primes 3 * 19 * 6445147 such that 3 + 19 + 6445147 = 6445169 is prime.
%p A385968 tcat:= proc(a,b,c);
%p A385968   c + 10^(1+ilog10(c))*(b + 10^(1+ilog10(b))*a)
%p A385968 end proc:
%p A385968 R:= NULL: count:= 0:
%p A385968 q:= 2: r:= 3:
%p A385968 while count < 100 do
%p A385968   p:= q; q:= r; r:= nextprime(r);
%p A385968   x:= tcat(p,q,r);
%p A385968   F:= ifactors(x)[2];
%p A385968   if add(t[2],t=F) = 3 and isprime(add(t[1]*t[2],t=F)) then
%p A385968      count:= count+1; R:= R,x;
%p A385968   fi;
%p A385968 od:
%p A385968 R;
%t A385968 tp[p_]:=FromDigits[Join[IntegerDigits/@{Prime[p],Prime[p+1],Prime[p+2]}//Flatten]];Select[Array[tp,530],PrimeOmega[#]==3&&PrimeQ[Total[First/@FactorInteger[#]]]&] (* _James C. McMahon_, Jul 20 2025 *)
%Y A385968 Intersection of A107707 and A383114.
%K A385968 nonn,base
%O A385968 1,1
%A A385968 _Will Gosnell_ and _Robert Israel_, Jul 13 2025