

A160217


Minimal increasing sequence with a(1)=3 and the property that a(n) and n are both in or both not in A003159.


5



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
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OFFSET

1,1


COMMENTS

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 mdependent minimum index.


LINKS

Table of n, a(n) for n=1..66.
V. Shevelev, Several results on sequences which are similar to the positive integers, arXiv:0904.2101 [math.NT], 2009.


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))=1A010060(n)
For n>=1, A010060(a(n))= A010060(A004760(n+1)). See also A160230. [Vladimir Shevelev, 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.


MATHEMATICA

a35263[n_] := 1  Mod[IntegerExponent[n, 2], 2];
a[1] = 3; a[n_] := a[n] = For[k = a[n  1] + 1, True, k++, If[a35263[k] == a35263[n], Return[k]]];
Array[a, 66] (* JeanFrançois Alcover, Jul 28 2018 *)


CROSSREFS

Cf. A003159, A007814, A010060, A160216, A159619.
Cf. A004760, A160230. [Vladimir Shevelev, May 05 2009]
Sequence in context: A289182 A188974 A047558 * A228014 A188971 A176065
Adjacent sequences: A160214 A160215 A160216 * A160218 A160219 A160220


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, May 04 2009


EXTENSIONS

Edited by R. J. Mathar, May 08 2009


STATUS

approved



