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

Author

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

Keywords

• easy
• nonn
• nice

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

Examples

			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.
		

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]

Crossrefs

Cf. A002808, A018252, A022449, A175251.

Programs

Haskell

a050435 = a002808 . a002808
a050435_list = map a002808 a002808_list
-- Reinhard Zumkeller, Jan 12 2013

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 *)

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

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

Extensions

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