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

199211223, 331337347, 367373379, 487491499, 653659661, 859863877, 102110311033, 106910871091, 111711231129, 112911511153, 130313071319, 143914471451, 165716631667, 178918011811, 214321532161, 226722692273, 246724732477, 274127492753, 274927532767, 284328512857, 330133073313, 362336313637

Offset: 1

Author

Will Gosnell and Robert Israel, Jul 13 2025

Keywords

• nonn
• base

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A107707 and A383114.

Programs

Maple

tcat:= proc(a,b,c);
  c + 10^(1+ilog10(c))*(b + 10^(1+ilog10(b))*a)
end proc:
R:= NULL: count:= 0:
q:= 2: r:= 3:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  x:= tcat(p,q,r);
  F:= ifactors(x)[2];
  if add(t[2],t=F) = 3 and isprime(add(t[1]*t[2],t=F)) then
     count:= count+1; R:= R,x;
  fi;
od:
R;

Mathematica

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 *)