

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
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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$10]], Q);
while count < 30 do
T:= extract(Q);
if T[1] = r + 1 then
R:= R, r; count:= count+1;
fi;
r:= T[1];
p:= T[2][1];
q:= nextprime(p);
for i from 10 to 1 by 1 while T[2][i] = p do
insert([r*(q/p)^(11i), [op(T[2][1..i1]), q$(11i)]], Q);
od
od:
R;


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



