A358438 a(1) = 4, a(2) = 6; then a(n + 1) is the smallest semiprime number > a(n) such that the sum of any three consecutive terms is a semiprime.

4, 6, 15, 25, 34, 35, 46, 62, 69, 74, 94, 106, 119, 121, 122, 134, 142, 146, 158, 169, 178, 206, 213, 214, 235, 249, 253, 265, 267, 299, 303, 319, 321, 334, 382, 395, 422, 445, 446, 454, 466, 469, 482, 514, 517, 538, 586, 589, 591, 623, 629

Offset: 1

Author

Zak Seidov, Nov 17 2022

Keywords

• nonn

Comments

Do even numbers thin out as you look at larger and larger numbers of terms? - Charles R Greathouse IV, Nov 18 2022

Examples

			4 + 6 + 15 = 25 = 5*5, 6 + 15 + 25 = 46 = 2*23.
		

Links

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

Crossrefs

Cf. A062391 (analog for primes), A001358 (semiprimes).

Programs

Maple

R:= 4,6:
for i from 3 to 100 do
  s:= R[i-2]+R[i-1];
  for t from R[i-1]+1 do
    if numtheory:-bigomega(t) = 2 and numtheory:-bigomega(s+t)=2 then
      R:= R, t; break
    fi
od od:
R; # Robert Israel, Nov 18 2022

Mathematica

s = {4, 6}; p = 4; q = 6; r = q + 1; Do[While[2 != PrimeOmega[r] || 2 != PrimeOmega[p + q + r], r++]; AppendTo[s, r]; p = q; q = r; r++, {100}]; s