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

1,1

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

Table of n, a(n) for n=1..35.

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.

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) & ]

Crossrefs

Cf. A065049, A065359.

Sequence in context: A234502 A089201 A292174 * A269486 A239272 A076574

Adjacent sequences: A065120 A065121 A065122 * A065124 A065125 A065126

Keyword

base,nonn,changed

Author

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

Extensions

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

Status

approved