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%I #11 Jul 17 2015 05:54:55
%S 2,3,4,8,9,16,18,32,33,36,64,65,66,72,128,129,130,132,144,256,258,260,
%T 264,265,288,289,512,513,516,520,528,530,576,578,1024,1025,1026,1032,
%U 1040,1056,1057,1060,1152,1156,2048,2049,2050,2052,2064,2080,2112,2114
%N Numbers having exactly one prime contained as binary substring in binary representation of n.
%C A078826(a(n)) = 1; A078830 is a subsequence;
%C for k>2 also floor(a(k)/2) belongs to the sequence.
%H Reinhard Zumkeller, <a href="/A078829/b078829.txt">Table of n, a(n) for n = 1..120</a>
%e n=18 -> '10010' contains only 1 distinct binary substring which is prime: '10' (10bbb or bbb10), therefore 18 is a term.
%t primeCount[n_] := (bits = IntegerDigits[n, 2]; lg = Length[bits]; Reap[Do[If[PrimeQ[p = FromDigits[bits[[i ;; j]], 2]], Sow[p]], {i, 1, lg-1}, {j, i+1, lg}]][[2, 1]] // Union // Length); primeCount[1] = 0; Select[Range[3000], primeCount[#] == 1 &] (* _Jean-François Alcover_, May 23 2013 *)
%o (Haskell)
%o a078829 n = a078829_list !! (n-1)
%o a078829_list = filter ((== 1) . a078826) [1..]
%o -- _Reinhard Zumkeller_, Jul 17 2015
%Y Cf. A078826, A078830, A007088.
%Y Cf. A225243.
%K nonn,base,nice
%O 1,1
%A _Reinhard Zumkeller_, Dec 08 2002
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