A208238 Smallest prime greater than n, containing it in binary representation.

2, 2, 5, 7, 17, 11, 13, 23, 17, 19, 41, 23, 89, 29, 29, 31, 67, 71, 37, 79, 41, 43, 89, 47, 97, 89, 53, 59, 113, 59, 61, 127, 131, 67, 137, 71, 73, 101, 307, 79, 163, 83, 337, 107, 89, 109, 349, 191, 97, 113, 101, 103, 211, 107, 109, 223, 113, 229, 233, 239

Offset: 0

Author

Reinhard Zumkeller, Feb 14 2013

Keywords

• nonn

Comments

a(n) <= A208241(n);

A174332(n) = a(A000040(n)).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A208241, A004676, A007088, A010051, A030308.

Programs

Haskell

import Data.List (genericIndex, find, isInfixOf)
import Data.Maybe (fromJust)
a208238 = genericIndex a208238_list
a208238_list = f nns $ filter ((== 1) . a010051' . fst) nns where
   f mms'@((m,ms):mms) pps'@((p,ps):pps) =
     if m == p then f mms' pps else q : f mms pps'
     where q = fst $ fromJust $ find ((ms `isInfixOf`) . snd) pps'
   nns = zip [0..] a030308_tabf

Mathematica

spgn[n_]:=Module[{idn2=IntegerDigits[n,2],p=NextPrime[n]},While[SequenceCount[ IntegerDigits[ p,2],idn2] == 0,p = NextPrime[p]];p]; Array[spgn,60,0] (* Harvey P. Dale, Dec 23 2023 *)