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%I #32 Feb 06 2024 23:02:29
%S 73,89,127,349,733,773,787,1201,1453,1553,1597,1657,1753,1759,1777,
%T 1783,1811,1889,1913
%N Dead-end primes in "The Prime Number Maze" reachable from 2.
%C Is it possible that this sequence is an incorrect version of A065092? - _Paul V. McKinney_, May 20 2022
%C No. This sequence is a list of values for which reaching a Mersenne prime according to the rules of the maze is impossible. For 73 the only available move is to swap to 89, and vice versa (although there are other ways of reaching them, for example 601 can transition to 89). While 127 is already a Mersenne prime, it is not possible to reach another Mersenne prime starting from 127. In addition, to be included in this sequence, the value must be reachable starting from 2 (cf. A365001 for removal of this restriction). However, I'm not convinced that the current terms are complete. For example, should 173 be in this sequence? - _Sean A. Irvine_, Aug 15 2023
%C 173 is of incorrect parity and therefore not reachable starting from 2. - _Paul V. McKinney_, Sep 21 2023
%H William Paulsen, <a href="http://myweb.astate.edu/wpaulsen/primemaze/pmaze.html">The Prime Maze</a>
%H William Paulsen, <a href="http://myweb.astate.edu/wpaulsen/primemaze/mazeisol.html">Are some rooms totally isolated?</a>
%H William Paulsen, <a href="https://www.fq.math.ca/Scanned/40-3/paulsen.pdf">The Prime Maze</a>, Fib. Quart., 40 (2002), 272-279.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/problems/prob_025.htm">Problem 25. The William Paulsen's Prime Numbers Maze</a>, The Prime Puzzles & Problems Connection.
%Y Cf. A365001.
%K base,nonn,more
%O 1,1
%A William Paulsen (wpaulsen(AT)csm.astate.edu), Nov 12 2001
%E Corrected by _T. D. Noe_, Nov 14 2006
%E Title clarified by _Sean A. Irvine_, Aug 15 2023
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