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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 Robert Israel, Table of n, a(n) for n = 1..10000 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 Cf. A001222, A046310, A046312, A115186, A369897. Sequence in context: A205891 A186532 A184455 * A210017 A176167 A248203 Adjacent sequences: A369895 A369896 A369897 * A369899 A369900 A369901 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.)