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

1,1

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.

Links

Table of n, a(n) for n=1..58.

Example

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.

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));

Crossrefs

Cf. A001358, A014612, A363353.

Sequence in context: A114914 A026046 A330191 * A256084 A039486 A092890

Adjacent sequences: A363349 A363350 A363351 * A363353 A363354 A363355

Keyword

nonn,base

Author

Robert Israel, Aug 16 2023

Status

approved