A050435 a(n) = composite(composite(n)), where composite = A002808, composite numbers.

9, 12, 15, 16, 18, 21, 24, 25, 26, 28, 32, 33, 34, 36, 38, 39, 40, 42, 45, 48, 49, 50, 51, 52, 55, 56, 57, 60, 63, 64, 65, 68, 69, 70, 72, 74, 76, 77, 78, 80, 81, 84, 86, 87, 88, 90, 91, 93, 94, 95, 98, 100, 102, 104, 105, 106, 110, 111, 112, 115, 116, 117, 118, 119

Offset

1,1

Comments

Second-order composite numbers.

Composites (A002808) with composite (A002808) subscripts. a(n) U A022449(n) = A002808(n). Subsequence of A175251 (composites (A002808) with nonprime (A018252) subscripts), a(n) = A175251(n+1) for n >= 1. - Jaroslav Krizek, Mar 14 2010

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

N. Fernandez, An order of primeness, F(p)

N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Formula

Let C(n) be the n-th composite number, with C(1)=4. Then these are numbers C(C(n)).

a(n) = n + 2n/log n + O(n/log^2 n). - Charles R Greathouse IV, Jun 25 2017

Example

The 2nd composite number is 6 and the 6th composite number is 12, so a(2) = 12. a(100) = A002808(A002808(100)) = A002808(133) = 174.

Mathematica

Select[ Range[ 6, 150 ], ! PrimeQ[ # ] && ! PrimeQ[ # - PrimePi[ # ] - 1 ] & ]
With[{cmps=Select[Range[200], CompositeQ]}, Table[cmps[[cmps[[n]]]], {n, 70}]] (* Harvey P. Dale, Feb 18 2018 *)

Prog

(Haskell)
a050435 = a002808 . a002808
a050435_list = map a002808 a002808_list
-- Reinhard Zumkeller, Jan 12 2013
(PARI) composite(n)=my(k=-1); while(-n + n += -k + k=primepi(n), ); n \\ M. F. Hasler
a(n)=composite(composite(n)) \\ Charles R Greathouse IV, Jun 25 2017
(Python)
from sympy import composite
def a(n): return composite(composite(n))
print([a(n) for n in range(1, 65)]) # Michael S. Branicky, Sep 12 2021

Crossrefs

Cf. A002808, A018252, A022449, A175251.

Sequence in context: A114306 A009188 A138299 * A176656 A377873 A369002

Adjacent sequences: A050432 A050433 A050434 * A050436 A050437 A050438

Keyword

easy,nonn,nice

Author

Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

Extensions

More terms from Robert G. Wilson v, Dec 20 2000

Status

approved