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A099628
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Numbers m where m-th Catalan number A000108(m)=C(2m,m)/(m+1) is divisible by 2 but not by 4, i.e. where A048881(m)=1.
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1
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2, 4, 5, 8, 9, 11, 16, 17, 19, 23, 32, 33, 35, 39, 47, 64, 65, 67, 71, 79, 95, 128, 129, 131, 135, 143, 159, 191, 256, 257, 259, 263, 271, 287, 319, 383, 512, 513, 515, 519, 527, 543, 575, 639, 767, 1024, 1025, 1027, 1031, 1039, 1055, 1087, 1151, 1279, 1535, 2048
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Also a(n)+1 and a(n)-1, written in binary, both have a 1 in exactly one corresponding position; BitAnd[a(n)-1,a(n)+1]==2^k with k positive. - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Nov 24 2007
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FORMULA
| As triangle, T(n, k) = 2^(n+1)+2^k-1 = A099627(n+1, k).
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EXAMPLE
| As triangle, rows start 2; 4,5; 8,9,11; 16,17,19,23; 32,33,35,39,47; etc.
5 is in the sequence since 10!/(5!6!) = 42 is divisible by 2 but not 4; 6 is not in the sequence since 12!/(6!7!) = 132 is divisible by 4; 7 is not in the sequence since 14!/(7!8!)=429 is not divisible by 2.
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MATHEMATICA
| Select[Range[2048], IntegerQ[Log[2, BitAnd[ #+1, #-1]]]&] - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Nov 24 2007
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CROSSREFS
| Sequence in context: A080148 A032787 A067366 * A188072 A189205 A137169
Adjacent sequences: A099625 A099626 A099627 * A099629 A099630 A099631
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Oct 25 2004
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