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A369898 Numbers k such that k and k + 1 each have 9 prime divisors, counted with multiplicity. 1
203391, 698624, 1245375, 1942784, 2176064, 2282175, 2536191, 2858624, 2953664, 3282687, 3560192, 3655935, 3914000, 4068224, 4135616, 4205600, 4244967, 4586624, 4695488, 4744575, 4991679, 5055615, 5450624, 5475519, 5519744, 6141824, 6246800, 6410096, 6655040, 6660224, 6753375, 6816879, 6862400 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers k such that k and k + 1 are in A046312.
If a and b are coprime terms of A046310, one of them even, then Dickson's conjecture implies there are infinitely many terms k where k/a and (k+1)/b are primes.
LINKS
EXAMPLE
a(3) = 1245375 is a term because 1245375 = 3^5 * 5^3 * 41 and 1245376 = 2^6 * 11 * 29 * 61 each have 9 prime factors, counted with multiplicity.
MAPLE
with(priqueue):
R:= NULL: count:= 0:
initialize(Q); r:= 0:
insert([-2^9, [2$9]], Q);
while count < 40 do
T:= extract(Q);
if -T[1] = r + 1 then
R:= R, r; count:= count+1;
fi;
r:= -T[1];
p:= T[2][-1];
q:= nextprime(p);
for i from 9 to 1 by -1 while T[2][i] = p do
insert([-r*(q/p)^(10-i), [op(T[2][1..i-1]), q$(10-i)]], Q);
od
od:
R;
CROSSREFS
Sequence in context: A205891 A186532 A184455 * A210017 A176167 A248203
KEYWORD
nonn
AUTHOR
Robert Israel, Feb 04 2024
STATUS
approved

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Last modified April 17 04:44 EDT 2024. Contains 371756 sequences. (Running on oeis4.)