| 3, 6, 7, 9, 11, 14, 15, 18, 19, 22, 23, 25, 27, 30, 31, 33, 35, 38, 39, 41, 43, 46, 47, 50, 51, 54, 55, 57, 59, 62, 63, 66, 67, 70, 71, 73, 75, 78, 79, 82, 83, 86, 87, 89, 91, 94, 95, 97, 99, 102, 103, 105, 107, 110, 111, 114, 115, 118, 119, 121, 123, 126, 127, 129, 131, 134
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The primes in this sequence give A160216.
Conjecture: Let m>3 belong to A003159. Define the sequence b(n) to be the minimal increasing sequence with b(1)=m and the property that b(n) and n are both in or both not in A003159. Then a(n)=b(n) for all n larger than some m-dependent minimum index.
|
|
LINKS
|
V. Shevelev, Several results on sequences which are similar to the positive integers, arXiv:0904.2101 [math.NT]
|
|
FORMULA
|
a(n+1)=min{ m>a(n): A035263(m)=A035263(n+1) }.
a(n)=2n+1, if A007814(n) is even. a(n)=2n+2, if A007814(n) is odd.
A010060(a(n))=1-A010060(n)
For n>=1, A010060(a(n))= A010060(A004760(n+1)). See also A160230. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 05 2009]
|
|
EXAMPLE
|
n=2 is not in A003159. So a(2) is the smallest number larger than a(1)=3 which is not in A003159. This excludes 4 and 5 which are in A003159 and leads to a(2)=6.
|
|
CROSSREFS
|
Cf. A003159, A007814, A010060, A160216, A159619.
Cf. A004760 A160230 [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 05 2009]
Sequence in context: A026415 A026406 A047558 this_sequence A135412 A082847 A047242
Adjacent sequences: A160214 A160215 A160216 this_sequence A160218 A160219 A160220
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 04 2009
|
|
EXTENSIONS
|
Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 08 2009
|
|
