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

1,2

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.

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

Formula

a(n) <= A000040(n).

Example

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_

Prog

(PARI) See Links section.

Crossrefs

Cf. A000040, A286417, A303076 (inverse).

Sequence in context: A082317 A163915 A163916 * A286417 A303076 A298847

Adjacent sequences: A303072 A303073 A303074 * A303076 A303077 A303078

Keyword

nonn,base,look

Author

Rémy Sigrist, Apr 18 2018

Status

approved