%I A138290
%S A138290 6,14,22,26,30,36,38,42,54,57,62,70,78,81,90,94,110,122,126,132,134,138,
%T A138290 142,147,150,158,166,168,171,172,174,178,182,190,194,198,206,210,222,
%U A138290 238,254,285,294,312,315,318,334,336,350,366,372,382,405,414,416,432
%N A138290 Numbers n such that 2^(n+1)-2^k-1 is composite for all 0 <= k < n.
%C A138290 The binary representation of 2^(n+1)-2^k-1 has n 1-bits and one 0-bit. 
               Note that prime n are very rare: 577 is the first and 5569 is the 
               second.
%H A138290 T. D. Noe, <a href="b138290.txt">Table of n, a(n) for n=1..275</a>
%F A138290 For these n, A095058(n)=0 and A110700(n)>1.
%e A138290 6 is here because 95, 111, 119, 123, 125 and 126 are all composite.
%t A138290 t={}; Do[num=2^(n+1)-1; k=0; While[k<n && !PrimeQ[num-2^k], k++ ]; If[k==n, 
               AppendTo[t,n]], {n,100}]; t
%Y A138290 Sequence in context: A063299 A110223 A125086 this_sequence A023057 A062316 
               A079299
%Y A138290 Adjacent sequences: A138287 A138288 A138289 this_sequence A138291 A138292 
               A138293
%K A138290 nonn
%O A138290 1,1
%A A138290 T. D. Noe (noe(AT)sspectra.com), Mar 13 2008