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A102615
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Nonprime numbers of order 2.
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5
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1, 8, 10, 14, 15, 16, 20, 22, 24, 25, 27, 30, 32, 33, 35, 36, 38, 39, 40, 44, 46, 48, 49, 50, 51, 54, 55, 56, 58, 62, 63, 64, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 82, 85, 86, 87, 88, 90, 92, 93, 94, 96, 99, 100, 102, 104, 105, 108, 110, 111, 114, 115, 116, 117, 118, 120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.
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. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 13 2010]
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EXAMPLE
| Nonprime(2) = 4.
Nonprime(4) = 8 the second entry.
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MATHEMATICA
| nonPrime[n_] := FixedPoint[n + PrimePi[ # ] &, n]; Nest[nonPrime, Range[66], 2] (from Robert G. Wilson v Feb 04 2005)
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PROG
| (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) }
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CROSSREFS
| Cf. A018252.
Sequence in context: A010916 A101764 A048591 * A030490 A076639 A100319
Adjacent sequences: A102612 A102613 A102614 * A102616 A102617 A102618
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Jan 31 2005
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 04 2005
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