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

0,1

Comments

a(n) <= A208241(n);

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

Links

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A047083 A327019 A035085 * A127413 A145344 A034438

Adjacent sequences: A208235 A208236 A208237 * A208239 A208240 A208241

Keyword

nonn

Author

Reinhard Zumkeller, Feb 14 2013

Status

approved