A014234 Largest prime <= 2^n.

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

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

T. D. Noe, Table of n, a(n) for n=1..1000

Fred Curtis, C++ program for A014234

Harry J. Smith, PrimePi2 - Computes the Prime Pi(x) counting function [Broken link]

Harry J. Smith, PrimePi2 - Computes the Prime Pi(x) counting function [Cached copy]

Maple

a:= n-> prevprime(2^n+1):
seq(a(n), n=1..40);  # Alois P. Heinz, Apr 23 2020

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
(PARI) a(n) = precprime(2^n) \\ Michel Marcus, Aug 08 2013

Crossrefs

Cf. A000079, A014210.

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

See comment for the relationship to A027611.

Sequence in context: A071899 A242389 A102644 * A124430 A002013 A171416

Adjacent sequences: A014231 A014232 A014233 * A014235 A014236 A014237

Keyword

nonn

Author

Jud McCranie

Extensions

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

Status

approved