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A270338 Primes whose decimal expansion contains only 3's and 4's, in which every 4 is preceded and followed by a 3.

%I A270338 #27 Apr 03 2023 10:36:13
%S A270338 3343,3433,33343,333433,334333,343333,343433,3333433,3343343,3343433,
%T A270338 3433333,34333333,333334333,333343343,333343433,333433343,333434333,
%U A270338 334334333,3333334343,3333433343,3334333333,3343334333,3343434343,3433434343,3434343433,33333333343
%N A270338 Primes whose decimal expansion contains only 3's and 4's, in which every 4 is preceded and followed by a 3.
%C A270338 A sequence related to A054356. These primes look like "EEhEEhEEE" when viewed upside down by rotation of 180 degrees (3343 - "EhEE", 3433 - "EEhE", 33343 - "EhEEE", 333433 - "EEhEEE").
%D A270338 Giorgio Balzarotti, Paolo P. Lava, Centotre curiosità matematiche, Hoepli, 2010, pp. 3-4.
%H A270338 Robert Israel, <a href="/A270338/b270338.txt">Table of n, a(n) for n = 1..10000</a>
%H A270338 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/13463.html">Prime Curios!: 47</a>
%H A270338 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/1166.html">Prime Curios!: 3343</a>
%p A270338 S:= {}:
%p A270338 for n from 3 to 16 do
%p A270338   for k from 1 to floor((n-1)/2) do
%p A270338      for r in combinat:-choose(n-1-k,k) do
%p A270338         L:=subsop(seq(t=(3,4),t=r),[3$(n-k)]);
%p A270338         x:= add(L[i]*10^(n-i),i=1..n);
%p A270338         if isprime(x) then S:= S union {x} fi
%p A270338 od od od:
%p A270338 sort(convert(S,list)); # _Robert Israel_, Mar 15 2016
%t A270338 Select[Flatten[Table[FromDigits/@Select[Tuples[{3,4},n],SequenceCount[ #,{3,4,3},Overlaps->True]==Count[#,4]&],{n,3,11}]],PrimeQ]//Sort (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 17 2016 *)
%o A270338 (Magma) [p: p in [3..33333333343 by 10] | (p mod 100 eq 33 or p mod 100 eq 43) and IsPrime(p) and Position(IntegerToString(p), IntegerToString(3)) eq 1 and Set(Intseq(p)) subset [3, 4] and not IntegerToString(44) in IntegerToString(p)];
%Y A270338 Cf. A054356. Subsequence of A020461.
%K A270338 nonn,base,dumb
%O A270338 1,1
%A A270338 _Arkadiusz Wesolowski_, Mar 15 2016