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

%I A208241 #15 Nov 15 2020 02:01:14
%S A208241 2,5,7,17,11,13,29,17,19,41,23,97,53,29,31,67,71,37,79,41,43,89,47,97,
%T A208241 101,53,109,113,59,61,127,131,67,137,71,73,149,307,79,163,83,337,173,
%U A208241 89,181,373,191,97,197,101,103,211,107,109,223,113,229,233,239
%N A208241 Smallest prime greater than n, with n as prefix in binary representation.
%C A208241 A208238(n) <= a(n);
%C A208241 A174332(n) = a(A000040(n)).
%H A208241 Reinhard Zumkeller, <a href="/A208241/b208241.txt">Table of n, a(n) for n = 1..10000</a>
%p A208241 A208241 := proc(n)
%p A208241     local nbin,len,suf,sufbin,pbin,p ;
%p A208241     nbin := convert(n,base,2) ;
%p A208241     for len from 1 do
%p A208241         for suf from 0 to 2^len-1 do
%p A208241             sufbin := convert(suf,base,2) ;
%p A208241             while nops(sufbin) < len do
%p A208241                 sufbin := [op(sufbin),0] ;
%p A208241             end do:
%p A208241             pbin := [op(sufbin),op(nbin)] ;
%p A208241             p := add( 2^(i-1)*op(i,pbin),i=1..nops(pbin) ) ;
%p A208241             if isprime(p) then
%p A208241                 return p ;
%p A208241             end if;
%p A208241         end do:
%p A208241     end do:
%p A208241 end proc:
%p A208241 seq(A208241(n),n=1..50) ; # _R. J. Mathar_, May 06 2017
%o A208241 (Haskell)
%o A208241 import Data.List (genericIndex, find, isPrefixOf)
%o A208241 import Data.Maybe (fromJust)
%o A208241 a208241 = genericIndex a208241_list
%o A208241 a208241_list = f nns $ filter ((== 1) . a010051' . fst) nns where
%o A208241    f mms'@((m,ms):mms) pps'@((p,ps):pps) =
%o A208241      if m == p then f mms' pps else q : f mms pps'
%o A208241      where q = fst $ fromJust $ find ((ms `isPrefixOf`) . snd) pps'
%o A208241    nns = zip [1..] $ map reverse $ tail a030308_tabf
%Y A208241 Cf. A208238, A004676, A007088, A010051, A030308, A055011 (iterated).
%Y A208241 Cf. A164022 (greater or equal).
%K A208241 nonn,base
%O A208241 1,1
%A A208241 _Reinhard Zumkeller_, Feb 14 2013