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A369897 Numbers k such that k and k + 1 each have 10 prime divisors, counted with multiplicity. 2
3290624, 4122495, 4402431, 5675264, 6608384, 6890624, 7914752, 8614592, 9454400, 11553920, 12613887, 13466816, 14493248, 14853375, 15473024, 16719615, 17494784, 18272384, 18309375, 22784895, 24890624, 25200800, 25869375, 25957503, 26903744, 26921727, 27510272, 28350080, 29761424, 31802624 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers k such that k and k + 1 are in A046314.
If a and b are coprime terms of A046312, 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(5) = 6608384 is a term because 6608384 = 2^9 * 12907 and 6608385 = 3^6 * 5 * 7^2 * 37 each have 10 prime divisors, counted with multiplicity.
MAPLE
with(priqueue):
R:= NULL: count:= 0:
initialize(Q); r:= 0:
insert([-2^10, [2$10]], Q);
while count < 30 do
T:= extract(Q);
if -T[1] = r + 1 then
R:= R, r; count:= count+1;
fi;
r:= -T[1];
p:= T[2][-1];
q:= nextprime(p);
for i from 10 to 1 by -1 while T[2][i] = p do
insert([-r*(q/p)^(11-i), [op(T[2][1..i-1]), q$(11-i)]], Q);
od
od:
R;
CROSSREFS
Sequence in context: A036471 A206316 A186959 * A186594 A244574 A250675
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Feb 04 2024
STATUS
approved

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Last modified May 19 13:25 EDT 2024. Contains 372694 sequences. (Running on oeis4.)