A065123 Primes which, although they have correct parity, are not in the prime number maze.

683, 2699, 2729, 2731, 6827, 8363, 8747, 8867, 10427, 10667, 10799, 10859, 10883, 10889, 10891, 10937, 10939, 10979, 10987, 11003, 11171, 11177, 11243, 11939, 12011, 12203, 14891, 15017, 15083, 17749, 21589, 21841, 23893, 27179, 27299

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

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.

Links

• Michael I. Hartley, Partitions in the prime number maze, Acta Arithmetica 105 (2002), 227-238.
• W. Paulsen, The Prime Maze, Fib. Quart., 40 (2002), 272-279.

Crossrefs

Cf. A065049, A065359.

Programs

Mathematica

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) & ]

Extensions

More terms from Robert G. Wilson v, Dec 15 2001