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

1,1

Links

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

Example

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.

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

Crossrefs

Cf. A001358.

Sequence in context: A097136 A049348 A282389 * A145775 A283958 A335637

Adjacent sequences: A361608 A361609 A361610 * A361612 A361613 A361614

Keyword

nonn

Author

Zak Seidov and Robert Israel, Mar 17 2023

Status

approved