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A102616 Nonprime numbers of order 3.

%I A102616 #18 Aug 12 2025 02:39:08
%S A102616 1,14,16,22,24,25,30,33,35,36,39,44,46,48,50,51,54,55,56,62,64,66,68,
%T A102616 69,70,75,76,77,80,85,86,87,90,92,93,94,96,100,102,104,105,108,111,
%U A102616 115,116,117,118,120,122,123,124,126,130,132,134,136,138,142,144,145,148,150
%N A102616 Nonprime numbers of order 3.
%C A102616 nps(n,1) -> list nonprime(n) or the sequence of nonprime numbers. nps(n,2) -> list nonprime(nonprime(n)) or nps of order 2. nps(n,3) -> list nonprime(nonprime(nonprime(n))) or npcs of order 3 ..... The order is the number of nestings - 1.
%e A102616 Nonprime(2) = 4.
%e A102616 Nonprime(4) = 8.
%e A102616 Nonprime(8) = 14, the 2nd entry.
%p A102616 # For Maple code for the prime/nonprime compound sequences (listed in cross-references) see A003622. - _N. J. A. Sloane_, Mar 30 2016
%t A102616 nonPrime[n_] := FixedPoint[n + PrimePi[ # ] &, n]; Nest[ nonPrime, Range[62], 3] (* _Robert G. Wilson v_, Feb 04 2005 *)
%o A102616 (PARI) \\ We perform nesting(s) with a loop.
%o A102616 cics(n,m) = { local(x,y,z); for(x=1,n, z=x; for(y=1,m+1, z=nonprime(z); ); print1(z",") ) }
%o A102616 nonprime(n) = { local(c,x); c=1; x=0; while(c <= n, x++; if(!isprime(x),c++); ); return(x) }
%Y A102616 Cf. A018252, A102615.
%Y A102616 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 A102616 nonn
%O A102616 1,2
%A A102616 _Cino Hilliard_, Jan 31 2005
%E A102616 Edited by _Robert G. Wilson v_, Feb 04 2005