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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 Robert Israel, Table of n, a(n) for n = 1..10000 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 Cf. A001222, A046312, A046314, A115186. Sequence in context: A036471 A206316 A186959 * A186594 A244574 A250675 Adjacent sequences: A369894 A369895 A369896 * A369898 A369899 A369900 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.)