A360549 a(n) is the least prime p not already in the sequence such that a(n-1) + p is a triprime; a(1) = 2.

2, 43, 7, 5, 3, 17, 11, 19, 23, 29, 13, 31, 37, 41, 61, 53, 71, 59, 79, 103, 67, 47, 83, 89, 97, 73, 101, 137, 107, 131, 113, 109, 127, 139, 151, 167, 149, 173, 181, 157, 197, 191, 163, 193, 211, 199, 227, 179, 223, 229, 241, 233, 349, 257, 251, 283, 307, 271, 263, 293, 281, 317, 239, 269, 313

Offset

1,1

Comments

Conjecture: every prime eventually appears in the sequence.

Links

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

Example

a(4) = 5 because 5 is a prime that has not yet occurred in the sequence, a(4) + 5 = 12 = 2^2^3 is a triprime; the only other prime (3) that has not yet occurred does not work because a(4) + 3 = 10 = 2*5 is not a triprime.

Maple

R:= 2: p:= 2: P:= select(isprime, [seq(i, i=3..10000, 2)]):
do
  found:= false;
  for k from 1 to nops(P) do
      q:= P[k];
      if numtheory:-bigomega(q+p) = 3 then
      found:= true; p:= q; R:= R, p; P:= subsop(k=NULL, P); break
    fi
  od;
  if not found then break fi;
od:
R;

Mathematica

s3={2}; p=2; Do[q=3; While[MemberQ[s3, q]||3!=PrimeOmega[p+q], q=NextPrime[q]]; AppendTo[s3, p=q], {999}]; s3 (* Vincenzo Librandi, Mar 04 2025 *)

Prog

(Magma) PrimeOmega := function(n)
    return &+[t[2] : t in Factorization(n)];
end function;
s3 := [2];
p := 2;
for i in [1..999] do
    q := 3;
    while (q in s3) or (PrimeOmega(p + q) ne 3) do
        q := NextPrime(q);
    end while;
    Append(~s3, q);
    p := q;
end for;
s3; // Vincenzo Librandi, Mar 04 2025

Crossrefs

Cf. A014612, A353408.

Sequence in context: A052078 A069544 A256285 * A268467 A236695 A085460

Adjacent sequences: A360546 A360547 A360548 * A360550 A360551 A360552

Keyword

nonn

Author

Zak Seidov and Robert Israel, Mar 04 2023

Status

approved