%I #50 Jun 03 2024 16:04:55

%S 2,3,7,13,31,61,127,251,509,1021,2039,4093,8191,16381,32749,65521,

%T 131071,262139,524287,1048573,2097143,4194301,8388593,16777213,

%U 33554393,67108859,134217689,268435399,536870909,1073741789,2147483647,4294967291,8589934583,17179869143,34359738337,68719476731,137438953447

%N Largest prime <= 2^n.

%C 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

%D D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 390.

%H T. D. Noe, <a href="/A014234/b014234.txt">Table of n, a(n) for n=1..1000</a>

%H Fred Curtis, <a href="/A014234/a014234_1.txt">C++ program for A014234</a>

%H Harry J. Smith, <a href="http://www.math.niu.edu/~rusin/known-math/98/pi_x">PrimePi2 - Computes the Prime Pi(x) counting function</a> [Broken link]

%H Harry J. Smith, <a href="/A014234/a014234.txt">PrimePi2 - Computes the Prime Pi(x) counting function</a> [Cached copy]

%p a:= n-> prevprime(2^n+1):

%p seq(a(n), n=1..40); # _Alois P. Heinz_, Apr 23 2020

%t PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; Table[ Abs[ PrevPrim[2^n]], {n, 1, 30} ]

%t Join[{2},NextPrime[2^Range[2,40],-1]] (* _Harvey P. Dale_, Jun 26 2011 *)

%o (C++) // see link above

%o (PARI) a(n) = precprime(2^n) \\ _Michel Marcus_, Aug 08 2013

%Y Cf. A000079, A014210.

%Y Cf. A013603 (2^n - a(n)).

%Y See comment for the relationship to A027611.

%Y These primes have indices A007053 = number of primes <= 2^n.

%Y The opposite is A104080, delta A092131, indices A372684.

%Y For squarefree instead of prime we have A372889, indices A143658.

%Y A036378 counts primes between powers of 2, A293697 adds them up.

%Y Cf. A035100, A130739, A211997.

%K nonn

%O 1,1

%A _Jud McCranie_

%E Terms for n=31, n=32 added by Fred Curtis (fred(AT)f2.org), Dec 08 2009