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

1,1

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.

Links

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

Example

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.

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

Crossrefs

Cf. A014613, A361073.

Sequence in context: A350284 A182461 A205065 * A185790 A185761 A205248

Adjacent sequences: A368075 A368076 A368077 * A368079 A368080 A368081

Keyword

nonn

Author

Zak Seidov and Robert Israel, Dec 11 2023

Status

approved