The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A118955 Numbers of the form 2^k + prime. 18

%I

%S 3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,23,24,25,27,29,30,31,

%T 32,33,34,35,37,38,39,41,42,43,44,45,47,48,49,51,53,54,55,57,59,60,61,

%U 62,63,65,66,67,68,69,71,72,73,74,75,77,79,80,81,83,84,85,87,89,90,91,93

%N Numbers of the form 2^k + prime.

%C A109925(a(n)) > 0, complement of A118954;

%C The lower density is at least 0.09368 (Pintz) and upper density is at most 0.49095 (Habsieger & Roblot). The density, if it exists, is called Romanov's constant. Romani conjectures that it is around 0.434. - _Charles R Greathouse IV_, Mar 12 2008

%H Charles R Greathouse IV, <a href="/A118955/b118955.txt">Table of n, a(n) for n = 1..10000</a>.

%H Laurent Habsieger and Xavier-Francois Roblot, <a href="http://journals.impan.gov.pl/aa/Inf/122-1-4.html">On integers of the form p + 2^k</a>, Acta Arithmetica 122:1 (2006), pp. 45-50.

%H J. Pintz, <a href="http://dx.doi.org/10.1007/s10474-006-0060-6">A note on Romanov's constant</a>, Acta Mathematica Hungarica 112:1-2 (2006), pp. 1-14.

%H F. Romani, <a href="http://dx.doi.org/10.1007/BF02576468">Computations concerning primes and powers of two</a>, Calcolo 20 (1983), pp. 319-336.

%t Select[Range[100], (For[r=False; k=1, #>k, k*=2, If[PrimeQ[#-k], r=True]]; r)& ] (* _Jean-François Alcover_, Dec 26 2013, after _Charles R Greathouse IV_ *)

%o (PARI) is(n)=my(k=1);while(n>k,if(isprime(n-k),return(1),k*=2));0 \\ _Charles R Greathouse IV_, Mar 12 2008

%o a118955 n = a118955_list !! (n-1)

%o a118955_list = filter f [1..] where

%o f x = any (== 1) \$ map (a010051 . (x -)) \$ takeWhile (< x) a000079_list

%o -- _Reinhard Zumkeller_, Jan 03 2014

%Y Subsequence of A081311; A118957 is a subsequence.

%Y Cf. A156695, A010051, A000079.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 07 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 15:11 EST 2020. Contains 338683 sequences. (Running on oeis4.)