|
| |
|
|
A014234
|
|
Largest prime <= 2^n.
|
|
37
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
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
|
|
|
REFERENCES
|
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 390.
|
|
|
LINKS
|
|
|
|
MAPLE
|
a:= n-> prevprime(2^n+1):
|
|
|
MATHEMATICA
|
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 *)
|
|
|
PROG
|
(C++) // see link above
|
|
|
CROSSREFS
|
See comment for the relationship to A027611.
These primes have indices A007053 = number of primes <= 2^n.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
Terms for n=31, n=32 added by Fred Curtis (fred(AT)f2.org), Dec 08 2009
|
|
|
STATUS
|
approved
|
| |
|
|
