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A014234
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Largest prime <= 2^n.
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37
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2, 3, 7, 13, 31, 61, 127, 251, 509, 1021, 2039, 4093, 8191, 16381, 32749, 65521, 131071, 262139, 524287, 1048573, 2097143, 4194301, 8388593, 16777213, 33554393, 67108859, 134217689, 268435399, 536870909, 1073741789, 2147483647, 4294967291, 8589934583, 17179869143, 34359738337, 68719476731, 137438953447
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OFFSET
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1,1
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COMMENTS
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For n>1 largest prime factor of the denominator of A027611(2^n) = 2^n*(2^n)-th harmonic number. - Alexander Adamchuk, Aug 02 2006
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REFERENCES
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D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 390.
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LINKS
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MAPLE
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a:= n-> prevprime(2^n+1):
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MATHEMATICA
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PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; Table[ Abs[ PrevPrim[2^n]], {n, 1, 30} ]
Join[{2}, NextPrime[2^Range[2, 40], -1]] (* Harvey P. Dale, Jun 26 2011 *)
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PROG
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(C++) // see link above
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CROSSREFS
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See comment for the relationship to A027611.
These primes have indices A007053 = number of primes <= 2^n.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Terms for n=31, n=32 added by Fred Curtis (fred(AT)f2.org), Dec 08 2009
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STATUS
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approved
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