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

%I A208238 #11 Dec 23 2023 13:56:57
%S A208238 2,2,5,7,17,11,13,23,17,19,41,23,89,29,29,31,67,71,37,79,41,43,89,47,
%T A208238 97,89,53,59,113,59,61,127,131,67,137,71,73,101,307,79,163,83,337,107,
%U A208238 89,109,349,191,97,113,101,103,211,107,109,223,113,229,233,239
%N A208238 Smallest prime greater than n, containing it in binary representation.
%C A208238 a(n) <= A208241(n);
%C A208238 A174332(n) = a(A000040(n)).
%H A208238 Reinhard Zumkeller, <a href="/A208238/b208238.txt">Table of n, a(n) for n = 0..10000</a>
%t A208238 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 *)
%o A208238 (Haskell)
%o A208238 import Data.List (genericIndex, find, isInfixOf)
%o A208238 import Data.Maybe (fromJust)
%o A208238 a208238 = genericIndex a208238_list
%o A208238 a208238_list = f nns $ filter ((== 1) . a010051' . fst) nns where
%o A208238    f mms'@((m,ms):mms) pps'@((p,ps):pps) =
%o A208238      if m == p then f mms' pps else q : f mms pps'
%o A208238      where q = fst $ fromJust $ find ((ms `isInfixOf`) . snd) pps'
%o A208238    nns = zip [0..] a030308_tabf
%Y A208238 Cf. A208241, A004676, A007088, A010051, A030308.
%K A208238 nonn
%O A208238 0,1
%A A208238 _Reinhard Zumkeller_, Feb 14 2013