cp's OEIS Frontend

A102615 Nonprime numbers of order 2.

%I A102615 #14 Apr 06 2016 12:47:52
%S A102615 1,8,10,14,15,16,20,22,24,25,27,30,32,33,35,36,38,39,40,44,46,48,49,
%T A102615 50,51,54,55,56,58,62,63,64,66,68,69,70,72,75,76,77,78,80,82,85,86,87,
%U A102615 88,90,92,93,94,96,99,100,102,104,105,108,110,111,114,115,116,117,118,120
%N A102615 Nonprime numbers of order 2.
%C A102615 nps(n,0) -> list nonprime(n) or the sequence of nonprime numbers. nps(n,1) -> list nonprime(nonprime(n)) or nps of order 1 nps(n,2) -> list nonprime(nonprime(nonprime(n))) or nps of order 2 ..... The order is the number of nestings - 1. We avoid the nestings in the script with a loop.
%C A102615 Nonprimes (A018252) with nonprime (A018252) subscripts. a(n) U A078782(n) = A018252(n), a(n+1) U A175250(n) = A018252(n) for n >= 1. a(n) = nonprime(nonprime(n)) = A018252(A018252(n)). a(4) = 14 because a(4) = b(b(4)) = b(8) = 14, b = nonprime. a(1) = 1, a(n) = nonprimes (A018252) with composite (A002808) subscripts for n >=2. [_Jaroslav Krizek_, Mar 13 2010]
%e A102615 Nonprime(2) = 4.
%e A102615 Nonprime(4) = 8 the second entry.
%p A102615 # For Maple code for the prime/nonprime compound sequences (listed in cross-references) see A003622.  - _N. J. A. Sloane_, Mar 30 2016
%t A102615 nonPrime[n_] := FixedPoint[n + PrimePi[ # ] &, n]; Nest[nonPrime, Range[66], 2] (* _Robert G. Wilson v_, Feb 04 2005 *)
%o A102615 (PARI) \We perform nesting(s) with a loop. cics(n,m) = { local(x,y,z); for(x=1,n, z=x; for(y=1,m+1, z=composite(z); ); print1(z",") ) } composite(n) = \ The n-th composite number. 1 is defined as a composite number. { local(c,x); c=1; x=0; while(c <= n, x++; if(!isprime(x),c++); ); return(x) }
%Y A102615 Cf. A018252.
%Y A102615 Let A = primes A000040, B = nonprimes A018252. The 2-level compounds are AA = A006450, AB = A007821, BA = A078782, BB = A102615. The 3-level compounds AAA, AAB, ..., BBB are A038580, A049078, A270792, A102617, A270794, A270796, A102216.
%K A102615 nonn
%O A102615 1,2
%A A102615 _Cino Hilliard_, Jan 31 2005
%E A102615 Edited by _Robert G. Wilson v_, Feb 04 2005