A078829 Numbers having exactly one prime contained as binary substring in binary representation of n.

2, 3, 4, 8, 9, 16, 18, 32, 33, 36, 64, 65, 66, 72, 128, 129, 130, 132, 144, 256, 258, 260, 264, 265, 288, 289, 512, 513, 516, 520, 528, 530, 576, 578, 1024, 1025, 1026, 1032, 1040, 1056, 1057, 1060, 1152, 1156, 2048, 2049, 2050, 2052, 2064, 2080, 2112, 2114

Offset: 1

Author

Reinhard Zumkeller, Dec 08 2002

Keywords

• nonn
• base
• nice

Comments

A078826(a(n)) = 1; A078830 is a subsequence;

for k>2 also floor(a(k)/2) belongs to the sequence.

Examples

			n=18 -> '10010' contains only 1 distinct binary substring which is prime: '10' (10bbb or bbb10), therefore 18 is a term.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..120

Crossrefs

Cf. A078826, A078830, A007088.

Cf. A225243.

Programs

Haskell

a078829 n = a078829_list !! (n-1)
a078829_list = filter ((== 1) . a078826) [1..]
-- Reinhard Zumkeller, Jul 17 2015

Mathematica

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 *)