|
%I #10 Aug 24 2023 10:15:33
%S 76,114,116,174,222,236,238,246,255,258,282,285,286,310,316,322,325,
%T 333,338,357,369,374,385,387,434,436,474,534,539,549,555,574,582,595,
%U 596,710,715,716,722,725,762,777,782,786,795,796,834,894,1034,1074,1076,1146,1158,1162,1182,1185,1194,1310
%N Triprimes that are the concatenation of a prime and a semiprime (in that order).
%C 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.
%e 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.
%p P[1]:= [2,3,5,7]:
%p for d from 2 to 3 do P[d]:= select(isprime,[seq(i,i=10^(d-1)+1..10^d-1,2)]) od:
%p for d from 1 to 3 do SP[d]:= select(t -> numtheory:-bigomega(t) = 2, [$10^(d-1).. 10^d-1]) od:
%p R:= {}:
%p for d from 2 to 4 do
%p for d1 from 1 to d-1 do
%p d2:= d-d1;
%p V:= select(t -> numtheory:-bigomega(t)=3, {seq(seq(dcat(a,b),a=P[d1]),b=SP[d2])});
%p R:= R union V;
%p od
%p od:
%p sort(convert(R,list));
%Y Cf. A001358, A014612, A363353.
%K nonn,base
%O 1,1
%A _Robert Israel_, Aug 16 2023
|
