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A109732 a(1) = 1; for n>1, a(n) is the smallest number not already present which is entailed by the rules (i) k present => 2k+1 present; (ii) 3k present => k present. 2
1, 3, 7, 15, 5, 11, 23, 31, 47, 63, 21, 43, 87, 29, 59, 95, 119, 127, 175, 191, 239, 255, 85, 171, 57, 19, 39, 13, 27, 9, 55, 79, 111, 37, 75, 25, 51, 17, 35, 71, 103, 115, 143, 151, 159, 53, 107, 207, 69, 139, 215, 223, 231, 77, 155, 279, 93, 187, 287, 303, 101, 203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Van der Poorten asks if every odd number is in the sequence. This seems very likely.

Odd numbers of the form 2^k+1 take a long time to appear; e.g. 2^12+1 appears at a(64607). - T. D. Noe, Aug 10 2005

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

T. D. Noe, Graph of first 1000 terms

MATHEMATICA

maxVal=1000; f[n_]:=Module[{lst={}, x=n}, While[x=2x+1; x<maxVal, AppendTo[lst, x]]; lst]; M={1}; pending=f[1]; While[Length[pending]>0, next=First[pending]; pending=Rest[pending]; If[ !MemberQ[M, next], AppendTo[M, next]; While[Mod[next, 3]==0 && !MemberQ[M, next/3], next=next/3; AppendTo[M, next]; pending=Union[pending, f[next]]]]]; M (Noe)

CROSSREFS

Sequence in context: A234042 A001203 A154883 * A114396 A102032 A086517

Adjacent sequences:  A109729 A109730 A109731 * A109733 A109734 A109735

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, prompted by a posting by Alf van der Poorten (alf(AT)math.mq.edu.au) to the Number Theory List, Aug 10 2005

EXTENSIONS

More terms from T. D. Noe, Aug 10 2005

STATUS

approved

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Last modified December 21 10:52 EST 2014. Contains 252305 sequences.