A383114 Triprimes that are concatenations of three consecutive primes.

357, 131719, 434753, 475359, 717379, 97101103, 101103107, 103107109, 109113127, 139149151, 151157163, 157163167, 163167173, 167173179, 173179181, 193197199, 197199211, 199211223, 227229233, 241251257, 281283293, 293307311, 331337347, 347349353, 367373379, 397401409, 461463467, 487491499

Offset: 1

Author

Will Gosnell and Robert Israel, May 23 2025

Keywords

• nonn
• base

Comments

Numbers that are the concatenation (in increasing order) of three consecutive primes and are the product of three primes, counted with multiplicity.

Examples

			a(3) = 434753 is a term because it is the concatenation of the consecutive primes 43, 47 and 53 and 434753 = 11^2 * 3593 is the product of three primes, counted with multiplicity.
		

Links

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

Crossrefs

Intersection of A014612 and A132903.

Programs

Maple

cat3:= proc(a,b,c)
  (a*10^(1+ilog10(b))+b)*10^(1+ilog10(c))+c
end proc:
select(t ->numtheory:-bigomega(t)=3, [seq(cat3(ithprime(i),ithprime(i+1),ithprime(i+2)),i=1..100)]);

Mathematica

p3[p_]:=FromDigits[Join[IntegerDigits[Prime[p]],IntegerDigits[Prime[p+1]],IntegerDigits[Prime[p+2]]]];Select[Array[p3,100],PrimeOmega[#]==3&] (* James C. McMahon, Jun 09 2025 *)