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URL: https://oeis.org/A360534

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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.
1
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, 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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 10 2023
STATUS
approved