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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.
1
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
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
Sequence in context: A350284 A182461 A205065 * A185790 A185761 A205248
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Dec 11 2023
STATUS
approved