A065123 - OEIS

%I #10 Jan 05 2025 19:51:36

%S 683,2699,2729,2731,6827,8363,8747,8867,10427,10667,10799,10859,10883,

%T 10889,10891,10937,10939,10979,10987,11003,11171,11177,11243,11939,

%U 12011,12203,14891,15017,15083,17749,21589,21841,23893,27179,27299

%N Primes which, although they have correct parity, are not in the prime number maze.

%C The prime number maze is a maze of prime numbers where two primes are connected if and only if their base 2 representations differ in just one bit.

%H Michael I. Hartley, <a href="https://doi.org/10.4064/aa105-3-2">Partitions in the prime number maze</a>, Acta Arithmetica 105 (2002), 227-238.

%H 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.

%t f[ n_ ] := Block[ {d = Reverse[ IntegerDigits[ n, 2 ] ], l = s = 0, k = 1}, l = Length[ d ]; While[ k < l + 1, s = s - (-1)^k*d[ [ k ] ]; k++ ]; Return[ s ] ]; Select[ Range[ 5, 40000, 2 ], PrimeQ[ # ] && EvenQ[ Count[ IntegerDigits[ #, 2 ], 1 ] ] != OddQ[ Mod[ #, 3 ] ] && (f[ # ] > 2 || f[ # ] < 1) & ]

%Y Cf. A065049, A065359.

%K base,nonn

%O 1,1

%A William Paulsen (wpaulsen(AT)csm.astate.edu), Nov 13 2001

%E More terms from _Robert G. Wilson v_, Dec 15 2001