|
Search: id:A018252
|
|
|
| A018252 |
|
The nonprime numbers (1 together with the composite numbers, A002808). |
|
+0
122
|
|
| 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
d(n)<>2 (cf. A000005). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 17 2009]
Number of prime divisors of n (counted with multiplicity)<>1. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 30 2009]
Largest nonprime<nth composite. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 29 2009]
The nonnegative nonprimes A141468 without zero; the natural nonprimes; the whole nonprimes; the counting nonprimes. If the nonprime numbers A141468 which are also the nonnegative integers A001477, then the nonprimes A141468 also called the nonnegative nonprimes. If the nonprime numbers A018252 which are also the natural (or whole or counting) numbers A000027, then the nonprimes A018252 also called the natural nonprimes, the whole nonprimes and the counting nonprimes. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 22 2009]
Smallest nonprime>nth nonnegative nonprime. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Dec 04 2009]
|
|
REFERENCES
|
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.
|
|
LINKS
|
N. J. A. Sloane, List of nonprimes up to 20000: Table of n, a(n) for n = 1..17738
Unknown, The n-th nonprime.
Eric Weisstein's World of Mathematics, Monica Set
Eric Weisstein's World of Mathematics, Suzanne Set
Index entries for "core" sequences
|
|
FORMULA
|
Let b(0)=n+pi(n) and b(n+1)=n+pi(b(n)), with pi(n)=A000720(n); then a(n) is the limit value of b(n). - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 08 2001
a(n) = A137621(A137624(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 30 2008
|
|
MAPLE
|
with(numtheory); sort(convert(convert([ seq(i, i=1..541) ], set) minus convert([ seq(ithprime(i), i=1..100) ], set), list));
seq(`if`(not isprime(n), n, NULL), n=1..88); [From Peter Luschny (peter(AT)luschny.de), Jul 29 2009]
|
|
MATHEMATICA
|
NonPrime[n_Integer] := FixedPoint[n + PrimePi[ # ] &, n + PrimePi[n]]; Table[ NonPrime[n], {n, 1, 75} ]
|
|
PROGRAM
|
(MAGMA) [n : n in [1..100] | not IsPrime(n) ];
Contribution from Michael Porter (michael_b_porter(AT)yahoo.com), Nov 06 2009: (Start)
(PARI) isA018252(n) = !isprime(n)
A018252(n) = {local(a, b); b=n; a=1; while(a!=b, a=b; b=n+primepi(a)); b} (End)
|
|
CROSSREFS
|
Cf. A000040, A002808.
Cf. A000005, A001222. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 30 2009]
Sequence in context: A133576 A088224 A002808 this_sequence A141468 A077091 A051035
Adjacent sequences: A018249 A018250 A018251 this_sequence A018253 A018254 A018255
Cf. A141468. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Dec 04 2009]
|
|
KEYWORD
|
nonn,nice,easy,core,new
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.003 seconds
|
