A360534 Lexicographically earliest sequence of distinct prime numbers such that among each pair of consecutive terms, the decimal expansion of the smallest term appears in that of the largest term.

2, 23, 3, 13, 113, 11, 211, 2111, 22111, 322111, 3221, 32213, 2213, 22133, 622133, 6221, 62213, 362213, 5362213, 5, 53, 353, 3533, 33533, 333533, 33353, 233353, 233, 2333, 23333, 323333, 3233333, 32333333, 632333333, 6323, 86323, 863, 3863, 33863, 1338637, 7

Offset

1,1

Comments

This sequence is infinite:

- if a(n) < 10^k, then 10^(k+1) and 10*a(n) + 1 are coprime,

- so, by Dirichlet's theorem on arithmetic progressions, there are infinitely many prime numbers of the form k*10^(k+1) + 10*a(n) + 1, and we can extend the sequence.

If we consider positive integers instead of prime numbers, then we obtain the powers of 10 (A011557).

Links

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

Rémy Sigrist, PARI program

Example

The first terms are:
  n   a(n)    a(n) aligned
  --  ------  ------------
   1       2        2
   2      23        23
   3       3         3
   4      13        13
   5     113       113
   6      11       11
   7     211      211
   8    2111      2111
   9   22111     22111
  10  322111    322111
  11    3221    3221
  12   32213    32213
  13    2213     2213
  14   22133    22133
  15  622133   622133

Prog

(PARI) See Links section.

Crossrefs

Cf. A011557, A030456, A335043.

Sequence in context: A359272 A107801 A262702 * A076653 A114008 A110354

Adjacent sequences: A360531 A360532 A360533 * A360535 A360536 A360537

Keyword

nonn,base

Author

Rémy Sigrist, Feb 10 2023

Status

approved