cp's OEIS Frontend

A365001 Primes from which it is not possible to reach a (different) Mersenne prime by toggling a single bit per step while still remaining prime at every step.

%I A365001 #21 Jan 05 2025 19:51:42
%S A365001 73,89,127,173,191,233,239,251,257,277,337,349,373,431,443,491,557,
%T A365001 653,683,701,733,761,769,773,787,853,907,911,971,1019,1093,1109,1117,
%U A365001 1193,1201,1237,1297,1301,1303,1361,1367,1373,1381,1399,1429,1453,1489,1493
%N A365001 Primes from which it is not possible to reach a (different) Mersenne prime by toggling a single bit per step while still remaining prime at every step.
%C A365001 These are "locations" in The Prime Number Maze from which it is not possible to reach a (different) Mersenne prime by successively toggling single bits (see Paulsen for exact rules). This differs from A065111 in that it contains locations, such as 2131099, which are not reachable from 2.
%H A365001 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a365/A365001.java">Java program</a> (github)
%H A365001 W. Paulsen, <a href="http://myweb.astate.edu/wpaulsen/primemaze/pmaze.html">The Prime Maze</a>
%H A365001 W. Paulsen, <a href="http://myweb.astate.edu/wpaulsen/primemaze/mazeisol.html">Are some rooms totally isolated?</a>
%H A365001 W. Paulsen, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/40-3/paulsen.pdf">The Prime Maze</a>, Fib. Quart., 40 (2002), 272-279.
%H A365001 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.
%e A365001 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.
%Y A365001 Cf. A065111 (reachable from 2), A065092 (singularly dead end primes).
%K A365001 nonn,base
%O A365001 1,1
%A A365001 _Sean A. Irvine_, Aug 15 2023
%E A365001 Missing terms inserted by _Andrew Howroyd_ and name clarified by _Sean A. Irvine_, Sep 21 2023