The On-Line Encyclopedia of Integer Sequences (OEIS)

A306581 revision #9

A306581

Lexicographically earliest sequence of distinct positive terms such that the binary representations of two consecutive terms can always been concatenated in some order, without leading zero, to produce the binary representation of a prime number.

1, 2, 3, 4, 5, 6, 11, 8, 7, 9, 13, 10, 17, 12, 25, 18, 23, 15, 14, 19, 20, 21, 26, 27, 31, 29, 16, 37, 34, 45, 22, 39, 28, 55, 46, 57, 35, 24, 43, 36, 47, 33, 32, 41, 38, 67, 30, 53, 42, 61, 40, 49, 48, 73, 50, 51, 59, 56, 69, 44, 63, 52, 77, 60, 79, 54, 65

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This sequence is the binary variant of A228323.

The sequence is well defined; the argument used to prove that A018800(n) always exists applies here also.

LINKS

Table of n, a(n) for n=1..67.

Rémy Sigrist, Colored scatterplot of (n, a(n)) for n = 1..10000 (where the color corresponds to the parity of a(n): red for odd, blue for even)

Rémy Sigrist, Colored scatterplot of (n, a(n)-n) for n = 1..1000000 (where the color corresponds to the parity of a(n)-n: red for odd, blue for even)

Rémy Sigrist, Scatterplot of the first 1000000 terms of the ordinal transform of n -> a(n)-n

Rémy Sigrist, PARI program for A306581