A050435 - OEIS

%I #28 Sep 12 2021 12:49:50

%S 9,12,15,16,18,21,24,25,26,28,32,33,34,36,38,39,40,42,45,48,49,50,51,

%T 52,55,56,57,60,63,64,65,68,69,70,72,74,76,77,78,80,81,84,86,87,88,90,

%U 91,93,94,95,98,100,102,104,105,106,110,111,112,115,116,117,118,119

%N a(n) = composite(composite(n)), where composite = A002808, composite numbers.

%C Second-order composite numbers.

%C 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

%H Reinhard Zumkeller, <a href="/A050435/b050435.txt">Table of n, a(n) for n = 1..10000</a>

%H N. Fernandez, <a href="http://www.borve.org/primeness/FOP.html">An order of primeness, F(p)</a>

%H N. Fernandez, <a href="/A006450/a006450.html">An order of primeness</a> [cached copy, included with permission of the author]

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

%F a(n) = n + 2n/log n + O(n/log^2 n). - _Charles R Greathouse IV_, Jun 25 2017

%e 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.

%t Select[ Range[ 6, 150 ], ! PrimeQ[ # ] && ! PrimeQ[ # - PrimePi[ # ] - 1 ] & ]

%t With[{cmps=Select[Range[200],CompositeQ]},Table[cmps[[cmps[[n]]]],{n,70}]] (* _Harvey P. Dale_, Feb 18 2018 *)

%o (Haskell)

%o a050435 = a002808 . a002808

%o a050435_list = map a002808 a002808_list

%o -- _Reinhard Zumkeller_, Jan 12 2013

%o (PARI) composite(n)=my(k=-1); while(-n + n += -k + k=primepi(n), ); n \\ _M. F. Hasler_

%o a(n)=composite(composite(n)) \\ _Charles R Greathouse IV_, Jun 25 2017

%o (Python)

%o from sympy import composite

%o def a(n): return composite(composite(n))

%o print([a(n) for n in range(1, 65)]) # _Michael S. Branicky_, Sep 12 2021

%Y Cf. A002808, A018252, A022449, A175251.

%K easy,nonn,nice

%O 1,1

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

%E More terms from _Robert G. Wilson v_, Dec 20 2000