A384638 Primes p such that the concatenations of three consecutive primes starting with p, in both forward and backwards orders, are triprimes.

43, 47, 97, 101, 151, 157, 167, 199, 281, 293, 487, 601, 607, 809, 839, 967, 1013, 1069, 1129, 1223, 1249, 1259, 1289, 1361, 1367, 1543, 1571, 1663, 1753, 1861, 1871, 1873, 1997, 2141, 2281, 2551, 2593, 2909, 3121, 3271, 3313, 3361, 3371, 3461, 3823, 3881, 3907, 4019, 4211, 4289, 4327, 4349, 4451, 4513

Offset

1,1

Comments

Primes p such that if q and r are the next two primes, both concatenations p||q||r and r||q||p have three prime factors, counted with multiplicity.

Links

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

Example

a(2) = 47 is a term because 47, 53, 59 are consecutive primes and both 475359 = 3 * 193 * 821 and 595347 = 3 * 191 * 1039 have three prime factors, counted with multiplicity.

Maple

cat3:= proc(a, b, c)
(a*10^(1+ilog10(b))+b)*10^(1+ilog10(c))+c
end proc;
R:= NULL: count:= 0: a:= 2: b:= 3: c:= 5:
for i from 1 while count < 100 do
  a:= b; b:= c; c:= nextprime(c);
  if numtheory:-bigomega(cat3(a, b, c)) = 3 and numtheory:-bigomega(cat3(c, b, a)) = 3 then
     R:= R, a; count:= count+1;
  fi
od:
R;

Mathematica

Select[Prime[Range[612]], PrimeOmega[FromDigits[Join[IntegerDigits[#], IntegerDigits[NextPrime[#]], IntegerDigits[NextPrime[#, 2]]]]]==3&&PrimeOmega[FromDigits[Join[IntegerDigits[NextPrime[#, 2]], IntegerDigits[NextPrime[#, 1]], IntegerDigits[#]]]]==3&] (* James C. McMahon, Jun 20 2025 *)

Crossrefs

Cf. A014612, A383114, A384636.

Sequence in context: A334094 A033230 A330981 * A180519 A118485 A165444

Adjacent sequences: A384635 A384636 A384637 * A384639 A384640 A384641

Keyword

nonn,base

Author

Will Gosnell and Robert Israel, Jun 05 2025

Status

approved