A363352 Triprimes that are the concatenation of a prime and a semiprime (in that order).

76, 114, 116, 174, 222, 236, 238, 246, 255, 258, 282, 285, 286, 310, 316, 322, 325, 333, 338, 357, 369, 374, 385, 387, 434, 436, 474, 534, 539, 549, 555, 574, 582, 595, 596, 710, 715, 716, 722, 725, 762, 777, 782, 786, 795, 796, 834, 894, 1034, 1074, 1076, 1146, 1158, 1162, 1182, 1185, 1194, 1310

Offset: 1

Author

Robert Israel, Aug 16 2023

Keywords

• nonn
• base

Comments

If p is a prime and the number of digits of 3*p is in A363353, then the concatenation of p and 3*p is a term. The first term of this type is a(2728) = 37111.

Examples

			a(3) = 116 is a term because 11 is a prime, 6 = 2*3 is a semiprime, and their concatenation 116 = 2^2 * 29 is a triprime.
		

Crossrefs

Cf. A001358, A014612, A363353.

Programs

Maple

P[1]:= [2,3,5,7]:
for d from 2 to 3 do P[d]:= select(isprime,[seq(i,i=10^(d-1)+1..10^d-1,2)]) od:
for d from 1 to 3 do SP[d]:= select(t -> numtheory:-bigomega(t) = 2, [$10^(d-1).. 10^d-1]) od:
R:= {}:
for d from 2 to 4 do
  for d1 from 1 to d-1 do
    d2:= d-d1;
    V:= select(t -> numtheory:-bigomega(t)=3, {seq(seq(dcat(a,b),a=P[d1]),b=SP[d2])});
    R:= R union V;
  od
od:
sort(convert(R,list));