Cyclops numbers

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A number is a cyclops number in a given base

b

(base 10 by default) if that number has only one instance of the digit 0, instance which appears precisely in the middle (the eye of the cyclops) of the number. (This obviously implies an odd number of digits.)

Base 2 cyclops numbers

A138148 Cyclops numbers with binary digits only. (Base 2 cyclops numbers.)

{0, 101, 11011, 1110111, 111101111, 11111011111, 1111110111111, 111111101111111, 11111111011111111, 1111111110111111111, 111111111101111111111, 11111111111011111111111, ...}

A129868 Binary palindromic numbers with only one 0 bit. ([Base 2] cyclops numbers A138148, converted to base 10.)

{0, 5, 27, 119, 495, 2015, 8127, 32639, 130815, 523775, 2096127, 8386559, 33550335, 134209535, 536854527, 2147450879, 8589869055, 34359607295, 137438691327, 549755289599, ...}

A138831

n

-th perfect number minus 1, written in base 2. (Subset of A138148, cyclops numbers with binary digits, only.)

{101, 11011, 111101111, 1111110111111, 1111111111110111111111111, 111111111111111101111111111111111, 1111111111111111110111111111111111111, ...}

Base 10 cyclops numbers

A134808 Base 10 cyclops numbers.

{0, 101, 102, 103, 104, 105, 106, 107, 108, 109, 201, 202, 203, 204, 205, 206, 207, 208, 209, 301, 302, 303, 304, 305, 306, 307, 308, 309, 401, 402, 403, 404, 405, 406, 407, 408, ...}

Sequences

• A162199 Cyclops odd numbers.
• A162198 Cyclops even numbers.

• A134809 Cyclops prime numbers.
• A160712 Cyclops composite numbers.
• A160725 Cyclops semiprimes.
• A183058 Cyclops Sophie-Germain primes.
• A183057 Cyclops emirps.

• A160717 Cyclops triangular numbers.
• A160711 Cyclops square numbers.

• A182809 Cyclops Fibonacci numbers.
• A182811 Cyclops Lucas numbers.

• A183056 Cyclops partition numbers.

• A138131 Cyclops palindromic numbers.
• A153806 Cyclops strobogrammatic numbers. (The same upside down, in base 10 using Hindu-Arabic numerals, i.e. strobogrammatic digits {0, 1, 6, 8, 9}.)

• A?????? Cyclops numbers with circular digits {0, 6, 8, 9}.
• A160561 Cyclops primes with circular digits {0, 6, 8, 9}.
• A?????? Cyclops composites with circular digits {0, 6, 8, 9}.