A361611 Lexicographically least increasing sequence of semiprimes a(n) such that a(n) - a(n-1) and a(n) + a(n-1) are also semiprimes.

4, 10, 25, 94, 115, 206, 221, 298, 391, 478, 511, 526, 551, 586, 655, 694, 703, 758, 779, 934, 949, 974, 989, 993, 1126, 1159, 1418, 1513, 1522, 1555, 1594, 1603, 1658, 1679, 1718, 1769, 2018, 2051, 2066, 2105, 2174, 2195, 2234, 2319, 2462, 2501, 2578, 2587, 2846, 2867, 2906, 2931, 2986, 3007

Offset: 1

Author

Zak Seidov and Robert Israel, Mar 17 2023

Keywords

• nonn

Examples

			a(3) = 25 because with a(2) = 10, 25, 25 - 10 = 15 and 25 + 10 = 35 are all semiprimes, and none of the semiprimes between 10 and 25 work.
		

Links

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

Crossrefs

Cf. A001358.

Programs

Maple

R:= 4: count:= 0: x:= 4:
for i from 5 while count < 100 do
  if andmap(t -> numtheory:-bigomega(t)=2, [i,i+x,i-x]) then
    R:= R,i; x:= i; count:= count+1
  fi
od:
R;

Mathematica

s = {m=4};Do[p = m + 4; While[{2, 2, 2} != PrimeOmega[{p, m + p, p -
m}], p++]; AppendTo[s, m = p], {100}]; s