A102616 Nonprime numbers of order 3.

1, 14, 16, 22, 24, 25, 30, 33, 35, 36, 39, 44, 46, 48, 50, 51, 54, 55, 56, 62, 64, 66, 68, 69, 70, 75, 76, 77, 80, 85, 86, 87, 90, 92, 93, 94, 96, 100, 102, 104, 105, 108, 111, 115, 116, 117, 118, 120, 122, 123, 124, 126, 130, 132, 134, 136, 138, 142, 144, 145, 148, 150

Offset: 1

Author

Cino Hilliard, Jan 31 2005

Keywords

• nonn

Comments

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.

Examples

			Nonprime(2) = 4.
Nonprime(4) = 8.
Nonprime(8) = 14, the 2nd entry.
		

Crossrefs

Cf. A018252, 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.

Programs

Maple

# For Maple code for the prime/nonprime compound sequences (listed in cross-references) see A003622. - N. J. A. Sloane, Mar 30 2016

Mathematica

nonPrime[n_] := FixedPoint[n + PrimePi[ # ] &, n]; Nest[ nonPrime, Range[62], 3] (* Robert G. Wilson v, Feb 04 2005 *)

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=nonprime(z); ); print1(z",") ) }
nonprime(n) = { local(c,x); c=1; x=0; while(c <= n, x++; if(!isprime(x),c++); ); return(x) }

Extensions

Edited by Robert G. Wilson v, Feb 04 2005