A208241 Smallest prime greater than n, with n as prefix in binary representation.

2, 5, 7, 17, 11, 13, 29, 17, 19, 41, 23, 97, 53, 29, 31, 67, 71, 37, 79, 41, 43, 89, 47, 97, 101, 53, 109, 113, 59, 61, 127, 131, 67, 137, 71, 73, 149, 307, 79, 163, 83, 337, 173, 89, 181, 373, 191, 97, 197, 101, 103, 211, 107, 109, 223, 113, 229, 233, 239

Offset: 1

Author

Reinhard Zumkeller, Feb 14 2013

Keywords

• nonn
• base

Comments

A208238(n) <= a(n);

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A208238, A004676, A007088, A010051, A030308, A055011 (iterated).

Cf. A164022 (greater or equal).

Programs

Haskell

import Data.List (genericIndex, find, isPrefixOf)
import Data.Maybe (fromJust)
a208241 = genericIndex a208241_list
a208241_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 `isPrefixOf`) . snd) pps'
   nns = zip [1..] $ map reverse $ tail a030308_tabf

Maple

A208241 := proc(n)
    local nbin,len,suf,sufbin,pbin,p ;
    nbin := convert(n,base,2) ;
    for len from 1 do
        for suf from 0 to 2^len-1 do
            sufbin := convert(suf,base,2) ;
            while nops(sufbin) < len do
                sufbin := [op(sufbin),0] ;
            end do:
            pbin := [op(sufbin),op(nbin)] ;
            p := add( 2^(i-1)*op(i,pbin),i=1..nops(pbin) ) ;
            if isprime(p) then
                return p ;
            end if;
        end do:
    end do:
end proc:
seq(A208241(n),n=1..50) ; # R. J. Mathar, May 06 2017