A321128 Single-digit numbers in the order in which they first appear in the decimal expansions of prime numbers, followed by the two-digit numbers in the order in which they appear, then the three-digit numbers, and so on.

2, 3, 5, 7, 1, 9, 4, 6, 8, 0, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 10, 12, 27, 39, 14, 49, 15, 51, 57, 16, 63, 18, 81, 91, 93, 99, 21, 22, 33, 24, 25, 26, 69, 77, 28, 30, 34, 35, 36, 38, 40, 42, 44, 45, 46, 48, 87

Offset

1,1

Comments

This sequence is a variant of A321043.

This sequence establishes a bijection from the positive integers to the nonnegative integers; see A320938 for the inverse.

Prime numbers appear in increasing order.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored scatterplot of the first 100000 terms

Rémy Sigrist, Scatterplot of the first 100000 terms of the analog for the Euler totient function (A000010)

Rémy Sigrist, PARI program for A321128

Example

The first terms, alongside the corresponding prime numbers, are:
  n   a(n)  Prime
  --  ----  -----
   1     2      2
   2     3      3
   3     5      5
   4     7      7
   5     1     11
   6     9     19
   7     4     41
   8     6     61
   9     8     83
  10     0    101
  11    11     11
  12    13     13
  ...
  30    89     89
  31    97     97
  32    10    101
  33    12    127
  34    27    127
  35    39    139
  36    14    149
  37    49    149

Prog

(PARI) See Links section.

Crossrefs

Cf. A000010, A000040, A320938 (inverse), A321043.

Sequence in context: A101987 A178743 A126052 * A130138 A171855 A130136

Adjacent sequences: A321125 A321126 A321127 * A321129 A321130 A321131

Keyword

nonn,base,look

Author

Rémy Sigrist, Oct 27 2018

Status

approved