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Search: id:A137824
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| A137824 |
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Index at which A137823(n) occurs first in A137822 (gaps in numbers m such that 3 | sum( Catalan(k), k=1..2m)). |
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+0
7
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| 1, 3, 2, 4, 12, 8, 16, 48, 32, 64, 192, 128, 256, 768, 512, 1024, 3072, 2048, 4096, 12288, 8192, 16384, 49152, 32768, 65536, 196608, 131072, 262144, 786432, 524288, 1048576, 3145728, 2097152, 4194304, 12582912, 8388608, 16777216, 50331648
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Other characterization of the sequence: concatenate pattern (1,3,2) multiplying it by 4 after each concatenation step. Or: Start with 1,3,2, then iteratively append the whole sequence obtained so far multiplied by 4^(length of the sequence divided by 3)
See A137822 and A137823 for more comments and formulae.
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FORMULA
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If n=2 (mod 3) then a(n) = 3*2^[2(n-1)/3]; else a(n) = 2^[(2(n-1)/3].
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PROGRAM
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(PARI) A137824(n) = if( n%3==2, 3, 1)<<(2*(n-1)\3)
(PARI) A137824(n) = for( i=1, #A137822, A137822[i]==A137823[n] & return(i))
(PARI) a=[1, 3, 2]; for( i=1, 5, a=concat( a, 4^(#a/3)*a )); a
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CROSSREFS
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Cf. A107755, A122983, A137821-A137823.
Sequence in context: A084793 A033820 A095259 this_sequence A019321 A019116 A082493
Adjacent sequences: A137821 A137822 A137823 this_sequence A137825 A137826 A137827
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KEYWORD
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nonn,easy
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), May 15 2008
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