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A091524
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a(m) is the multiplier of sqrt(2) in the constant alpha(m) = a(m)*sqrt(2)-b(m), where alpha(m) is the value of the constant determined by the binary bits in the recurrence associated with the Graham-Pollak sequence.
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1
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1, 1, 2, 2, 3, 4, 3, 5, 4, 6, 7, 5, 8, 6, 9, 7, 10, 11, 8, 12, 9, 13, 14, 10, 15, 11, 16, 12, 17, 18, 13, 19, 14, 20, 21, 15, 22, 16, 23, 24, 17, 25, 18, 26, 19, 27, 28, 20, 29, 21, 30, 31, 22, 32, 23, 33, 24, 34, 35, 25, 36, 26, 37, 38, 27, 39, 28, 40, 41, 29, 42, 30, 43, 31, 44
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Each integer appears twice. If one deletes the first occurrence of each positive integer one obtains the sequence of positive integers : 1,2,3,4,5,... i.e. if we enclose in parentheses the first occurrence of 1,2,3,... giving (1),1,(2),2,(3),(4),3,(5),4,(6),(7),5,(8),6,(9),7,(10),.... and remove them, we obtain: 1,2,3,4,5,6,7,... The same property holds if one deletes the second occurrence of each positive integer. - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 13 2007
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LINKS
| Eric Weisstein's World of Mathematics, Graham-Pollak Sequence
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FORMULA
| Sequence is completely defined by : a(floor(n*(1+sqrt(2))))=n ; a(floor(n*(1+1/sqrt(2))))=n n>=1 since A003151 and A003152 are Beatty sequences partitioning the integers. - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 13 2007
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EXAMPLE
| -1+sqrt(2), -1+sqrt(2), -2+2sqrt(2), -2+2sqrt(2), -4+3sqrt(2), ..., so the sequence of multipliers is 1, 1, 2, 2, 3, ...
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CROSSREFS
| Cf. A001521.
Cf. A003151, A003152.
Sequence in context: A187199 A026254 A091525 * A026350 A205002 A165634
Adjacent sequences: A091521 A091522 A091523 * A091525 A091526 A091527
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Jan 18, 2004
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