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A359664 Prime Maze Room 11, opposite parity of A059459 starting from prime room 11.

%I A359664 #79 Feb 03 2023 16:25:28
%S A359664 11,43,41,2089,2081,2083,2087,
%T A359664 10889035741470030830827987437816582768679,
%U A359664 10889035741470030830827987437816582768647
%N A359664 Prime Maze Room 11, opposite parity of A059459 starting from prime room 11.
%C A359664 This is the opposite parity sequence of A059459 and lexicographically least of this sequence.
%C A359664 It is currently not known whether both of these sequences are infinite.
%C A359664 I was able to calculate 40 terms; a(40) is a 3261-digit prime.
%C A359664 a(1) = 11; a(n+1) is obtained by writing a(n) in binary and trying to complement just one bit, starting with the least significant bit, until a new prime is reached. (Terms 2 and 3 are excluded values from the main sequence.)
%C A359664 Conjecture: Room 2 and Room 11 are unlinked, i.e., two separate mazes or branches/trees, as they are of opposite parities.
%H A359664 Gregory Allen, <a href="/A359664/a359664_1.txt">Table of n, a(n) for n = 1..40</a>
%H A359664 William Paulsen, <a href="http://myweb.astate.edu/wpaulsen/primemaze/pmaze.html">Prime Maze</a>, See Prime room 11.
%H A359664 Carlos Rivera, <a href="http://www.primepuzzles.net/problems/prob_025.htm">Problem 25. William Paulsen's Prime Numbers Maze</a>, The Prime Puzzles and Problems Connection.
%t A359664 maxBits = 2^14;
%t A359664 ClearAll[a];
%t A359664 a[1] = 3;
%t A359664 a[2] = 2;
%t A359664 a[3] = 11;
%t A359664 n = 4;
%t A359664 a[n_] :=
%t A359664  a[n] = If[PrimeQ[a[n - 1]],
%t A359664    bits = PadLeft[IntegerDigits[a[n - 1], 2], maxBits];
%t A359664    For[i = 1, i <= maxBits, i++, bits2 = bits;
%t A359664     bits2[[-i]] = 1 - bits[[-i]];
%t A359664     If[i == maxBits, Print["maxBits reached"]; Break[],
%t A359664      If[PrimeQ[an = FromDigits[bits2, 2]] &&
%t A359664        FreeQ[Table[a[k], {k, 1, n - 1}], an], Return[an]]]],
%t A359664    0]; Table[a[n], {n, 42}]
%Y A359664 Cf. A059459.
%K A359664 nonn,less
%O A359664 1,1
%A A359664 _Gregory Allen_, Jan 10 2023