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Search: id:A138290
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| A138290 |
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Numbers n such that 2^(n+1)-2^k-1 is composite for all 0 <= k < n. |
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+0
2
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| 6, 14, 22, 26, 30, 36, 38, 42, 54, 57, 62, 70, 78, 81, 90, 94, 110, 122, 126, 132, 134, 138, 142, 147, 150, 158, 166, 168, 171, 172, 174, 178, 182, 190, 194, 198, 206, 210, 222, 238, 254, 285, 294, 312, 315, 318, 334, 336, 350, 366, 372, 382, 405, 414, 416, 432
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The binary representation of 2^(n+1)-2^k-1 has n 1-bits and one 0-bit. Note that prime n are very rare: 577 is the first and 5569 is the second.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..275
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FORMULA
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For these n, A095058(n)=0 and A110700(n)>1.
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EXAMPLE
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6 is here because 95, 111, 119, 123, 125, and 126 are all composite.
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MATHEMATICA
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t={}; Do[num=2^(n+1)-1; k=0; While[k<n && !PrimeQ[num-2^k], k++ ]; If[k==n, AppendTo[t, n]], {n, 100}]; t
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CROSSREFS
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Sequence in context: A063299 A110223 A125086 this_sequence A023057 A062316 A079299
Adjacent sequences: A138287 A138288 A138289 this_sequence A138291 A138292 A138293
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Mar 13 2008
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