A066195 Smallest prime containing n zeros in its binary expansion.

3, 2, 19, 17, 67, 131, 523, 257, 1033, 2053, 4099, 8209, 16417, 32771, 65539, 65537, 262147, 524353, 1048609, 2097169, 4194433, 8388617, 16777729, 67108913, 67239937, 134250497, 268435459, 536903681, 1073741827, 2147483713, 8589934627, 8589934609, 17179869697

Offset: 0

Author

Robert G. Wilson v, Dec 15 2001

Keywords

• base
• nonn

Comments

A023416(a(n)) = n and A023416(m) <> n for m < A049084(a(m)).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A061712.

Programs

Haskell

import Data.List (find)
import Data.Maybe (fromJust)
a066195 n = fromJust $ find ((== n) . a023416) a000040_list
-- Reinhard Zumkeller, Feb 19 2013

Mathematica

Do[ k = 1; While[ Count[ IntegerDigits[ Prime[ k ], 2 ], 0 ] != n, k++ ]; Print[ Prime[ k ] ], {n, 1, 24} ]

Extensions

a(25)-a(32) from Alois P. Heinz, Jun 28 2015