A368078 Lexicographically earliest increasing sequence a(n) of products of 4 primes such that a(n) - a(n-1) and a(n) + a(n-1) are also products of 4 primes. The 4 primes are counted with multiplicity.

16, 40, 100, 250, 558, 852, 1062, 1078, 1628, 1644, 1794, 2004, 2020, 2152, 2292, 2418, 2650, 2706, 2796, 2812, 3032, 3116, 3736, 3796, 3896, 3956, 3972, 4026, 4450, 4466, 4794, 5054, 5094, 5150, 5525, 5661, 5697, 5925, 6201, 6225, 6325, 6550, 6566, 6606, 6756, 6856, 6956, 7016, 7076, 8030, 8214

Offset: 1

Author

Zak Seidov and Robert Israel, Dec 11 2023

Keywords

• nonn

Comments

a(n) is the least number k > a(n-1) such that k, k - a(n-1), and k + a(n-1) are all in A014613.

Examples

			a(3) = 100 because a(2) = 40 and 100 = 2^2 * 5^2, 100 - 40 = 60 = 2^2 * 3 * 5 and 100 + 40 = 140 = 2^2 * 4 * 7 are all in A014613.
		

Links

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

Crossrefs

Cf. A014613, A361073.

Programs

Maple

isA014613:= proc(n) option remember; numtheory:-bigomega(n) = 4 end proc:
R:= 16: a:= 16: count:= 1:
while count < 100 do
  for x from a+16 do
    if isA014613(x-a) and isA014613(x) and isA014613(x+a) then break fi
  od;
  R:= R,x; a:= x; count:= count+1;
od:
R;

Mathematica

s = {m = 16}; Do[p = m + 16; While[{4, 4, 4} != PrimeOmega[{p, m +
p, p - m}], p++]; AppendTo[s, m = p], {50}]; s