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A357489
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Numbers k such that the k-th composition in standard order is a triple (w,x,y) such that 2w = 3x + 4y.
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4
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133, 1034, 4113, 8212, 32802, 65576, 131137, 262212, 524368, 1048706, 2097288, 4194464, 4194561, 8388868, 16777488, 33554752, 33554946, 67109384, 134218272, 134218753, 268436096, 268436484, 536871952, 1073742912, 1073743874, 2147484928, 2147485704, 4294969376
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OFFSET
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1,1
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COMMENTS
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A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
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LINKS
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EXAMPLE
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The terms together with the corresponding standard compositions begin:
133: (5,2,1)
1034: (7,2,2)
4113: (8,4,1)
8212: (9,2,3)
32802: (10,4,2)
65576: (11,2,4)
131137: (11,6,1)
262212: (12,4,3)
524368: (13,2,5)
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MATHEMATICA
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stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 10000], Length[stc[#]]==3&&2*stc[#][[1]]==3*stc[#][[2]]+4*stc[#][[3]]&]
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PROG
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(Python)
from itertools import count, islice
def A357489_gen(): # generator of terms
for n in count(1):
yield from sorted((1<<n-1)+(1<<x+(y:=m//6)-1)+(1<<y-1) for x in range(1, n) if (m:=2*n-5*x)>0 and 6*(n-x)>m and m%6==0)
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CROSSREFS
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See link for sequences related to standard compositions.
By sum, these triples appear to be counted by A008676.
A066099 lists the standard compositions.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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