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A124317 Semiprimes indexed by 3-almost primes. 3
22, 34, 51, 57, 82, 85, 87, 123, 133, 134, 146, 158, 201, 205, 209, 214, 221, 226, 237, 295, 305, 309, 321, 327, 341, 361, 365, 371, 394, 395, 413, 447, 478, 481, 497, 501, 529, 533, 543, 545, 551, 554, 559, 583, 597, 614, 623, 635, 689, 699, 734, 763, 766 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note that a(10)-a(9) = a(30)-a(29) = 1, achieving the minimum possible, due to a combination of the appropriate semiprime gap (A065516) and 3-almost prime gap (A114403).

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = semiprime(3almostprime(n)) = A001358(A014612(n)).

EXAMPLE

a(1) = semiprime(3almostprime(1)) = semiprime(8 = 2^3) = 22 = 2 * 11.

a(2) = semiprime(3almostprime(2)) = semiprime(12 = 2^2 * 3) = 34 = 2 * 17.

a(3) = semiprime(3almostprime(3)) = semiprime(18 = 2 * 3^2) = 51 = 3 * 17.

MATHEMATICA

p[k_] := Select[Range[1000], PrimeOmega[#] == k &]; p[2][[Take[p[3], 60]]] (* Giovanni Resta, Jun 13 2016 *)

CROSSREFS

Cf. A124318 3-almost primes indexed by semiprimes. A124319 semiprime(3almostprime(n)) - 3almostprime(semiprime(n)). A124308 Primes indexed by 5-almost primes. A124309 5-almost primes indexed by primes. A124310 prime(5almostprime(n)) - 5almostprime(prime(n)). 4-almost primes indexed by primes = A124283. prime(4almostprime(n)) - 4almostprime(prime(n)) = A124284. Primes indexed by 3-almost primes = A124268. 3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040, A001358] at n.

Cf. A000040, A001358, A014612, A065516, A114403, A122824, A124269, A124270, A124282-A124284, A124309, A124310, A124318, A124319.

Sequence in context: A306882 A125526 A181177 * A254691 A159518 A245365

Adjacent sequences:  A124314 A124315 A124316 * A124318 A124319 A124320

KEYWORD

easy,nonn,less

AUTHOR

Jonathan Vos Post, Oct 26 2006

EXTENSIONS

Data corrected by Giovanni Resta, Jun 13 2016

STATUS

approved

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Last modified October 21 01:18 EDT 2019. Contains 328291 sequences. (Running on oeis4.)