A303075 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the binary digits of a(n) appear in order but not necessarily as consecutive digits in the binary representation of the n-th prime number.

1, 3, 2, 7, 5, 6, 4, 9, 11, 13, 15, 8, 10, 19, 23, 12, 14, 29, 16, 17, 18, 31, 20, 21, 24, 25, 27, 26, 22, 28, 63, 32, 33, 34, 35, 37, 30, 40, 39, 38, 41, 42, 47, 48, 49, 51, 43, 55, 56, 50, 52, 59, 57, 61, 64, 65, 45, 67, 36, 44, 69, 53, 73, 71, 46, 62, 75

Offset: 1

Author

Rémy Sigrist, Apr 18 2018

Keywords

• nonn
• base
• look

Comments

This sequence is a permutation of the natural numbers with inverse A303076.

This sequence has similarities with A286417; there binary digits have to be consecutive, here not.

Examples

			The first terms, alongside the binary representations of the n-th prime and of a(n), are:
  n   a(n)  bin(p_n)    bin(a(n))
  --  ----  --------    ---------
   1     1        10        1_
   2     3        11        11
   3     2       101       10_
   4     7       111       111
   5     5      1011      101_
   6     6      1101      110_
   7     4     10001     100__
   8     9     10011     1001_
   9    11     10111     1011_
  10    13     11101     11_01
  11    15     11111     1111_
  12     8    100101    100_0_
  13    10    101001    1010__
  14    19    101011    10_011
  15    23    101111    10111_
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A303075
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000040, A286417, A303076 (inverse).

Programs

PARI

See Links section.

Formula

a(n) <= A000040(n).