

A161850


Subsequence of A161986 consisting of all terms that are prime.


2



7, 11, 13, 17, 19, 23, 29, 31, 37, 37, 41, 43, 47, 47, 53, 53, 59, 61, 67, 71, 71, 73, 79, 83, 89, 89, 97, 97, 101, 101, 103, 107, 109, 113, 127, 131, 137, 137, 139, 149, 149, 151, 157, 163, 163, 167, 167, 173, 179, 179, 181, 193, 191, 193, 197, 199, 211, 223, 227
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OFFSET

1,1


COMMENTS

A161986(n) = k+r where k is nth composite and r is remainder of (largest prime divisor of k) divided by (smallest prime divisor k).


LINKS

Table of n, a(n) for n=1..59.


EXAMPLE

A161986(1) to A161986(27) are 4, 7, 8, 9, 11, 13, 15, 17, 16, 19, 21, 22, 23, 25, 25, 27, 27, 29, 31, 32, 35, 35, 37, 37, 39, 40, 41. Hence a(1) to a(11) are the prime terms among them, namely 7, 11, 13, 17, 19, 23, 29, 31 ,37, 37, 41.


PROG

(MAGMA) [ p: n in [2..230]  not IsPrime(n) and IsPrime(p) where p is n+D[ #D] mod D[1] where D is PrimeDivisors(n) ];


CROSSREFS

Cf. A161986 (A002808(n)+A161849(n)), A002808 (composite numbers), A161849 (A052369(n) mod A056608(n)), A052369 (largest prime factor of nth composite), A056608 (smallest divisor of nth composite).
Sequence in context: A128974 A286609 A005776 * A007775 A070884 A135777
Adjacent sequences: A161847 A161848 A161849 * A161851 A161852 A161853


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Jun 20 2009


EXTENSIONS

Edited and corrected (a(19)=57 replaced by 67; a(38)=137, a(49)=179, a(50)=179 inserted) by Klaus Brockhaus, Jun 24 2009


STATUS

approved



