

A118955


Numbers of the form 2^k + prime.


18



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, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 79, 80, 81, 83, 84, 85, 87, 89, 90, 91, 93
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OFFSET

1,1


COMMENTS

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


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000.
Laurent Habsieger and XavierFrancois Roblot, On integers of the form p + 2^k, Acta Arithmetica 122:1 (2006), pp. 4550.
J. Pintz, A note on Romanov's constant, Acta Mathematica Hungarica 112:12 (2006), pp. 114.
F. Romani, Computations concerning primes and powers of two, Calcolo 20 (1983), pp. 319336.


MATHEMATICA

Select[Range[100], (For[r=False; k=1, #>k, k*=2, If[PrimeQ[#k], r=True]]; r)& ] (* JeanFrançois Alcover, Dec 26 2013, after Charles R Greathouse IV *)


PROG

(PARI) is(n)=my(k=1); while(n>k, if(isprime(nk), return(1), k*=2)); 0 \\ Charles R Greathouse IV, Mar 12 2008
(Haskell)
a118955 n = a118955_list !! (n1)
a118955_list = filter f [1..] where
f x = any (== 1) $ map (a010051 . (x )) $ takeWhile (< x) a000079_list
 Reinhard Zumkeller, Jan 03 2014


CROSSREFS

Subsequence of A081311; A118957 is a subsequence.
Cf. A156695, A010051, A000079.
Sequence in context: A029674 A192452 A132147 * A191838 A108473 A298113
Adjacent sequences: A118952 A118953 A118954 * A118956 A118957 A118958


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, May 07 2006


STATUS

approved



