

A218044


Numbers of the form 2^k + prime, with k > 0.


1



4, 5, 6, 7, 9, 10, 11, 13, 15, 17, 18, 19, 21, 23, 25, 27, 29, 31, 33, 34, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 66, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119
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OFFSET

1,1


COMMENTS

A039669 is included in this sequence.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
P. Erdõs, On integers of the form 2^k + p and some related problems, Summa Brasil. Math. 2 (1950), pp. 113123.
YongGao Chena and XueGong Sunb, On Romanoff's constant, Journal of Number Theory, Volume 106, Issue 2, June 2004, Pages 275284.
N. P. Romanoff, Über einige Sätze der additiven Zahlentheorie, Math. Ann. 57 (1934) 668678.


EXAMPLE

5 = 3 + 2 that is, a prime and a power of 2.


MATHEMATICA

nn = 119; ps = Prime[Range[PrimePi[nn]]]; p2 = 2^Range[Log[2, nn]]; u = {}; Do[u = Union[u, ps + p2[[i]]], {i, Length[p2]}]; Select[u, # <= nn &] (* T. D. Noe, Oct 19 2012 *)


PROG

(PARI) isok(n) = {forprime(p=2, n, my(d = n  p); if ((d==2)  (ispower(d, , &k) && (k==2)), return(1)); ); 0; } \\ Michel Marcus, Apr 18 2016


CROSSREFS

Cf. A080340, A039669, A118955 (allows k=0).
Sequence in context: A242337 A201739 A329782 * A066485 A079445 A120173
Adjacent sequences: A218041 A218042 A218043 * A218045 A218046 A218047


KEYWORD

nonn,easy


AUTHOR

Michel Marcus, Oct 19 2012


STATUS

approved



