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%I #10 Feb 12 2023 10:05:53
%S 2,23,3,13,113,11,211,2111,22111,322111,3221,32213,2213,22133,622133,
%T 6221,62213,362213,5362213,5,53,353,3533,33533,333533,33353,233353,
%U 233,2333,23333,323333,3233333,32333333,632333333,6323,86323,863,3863,33863,1338637,7
%N 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.
%C This sequence is infinite:
%C - if a(n) < 10^k, then 10^(k+1) and 10*a(n) + 1 are coprime,
%C - 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.
%C If we consider positive integers instead of prime numbers, then we obtain the powers of 10 (A011557).
%H Rémy Sigrist, <a href="/A360534/b360534.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A360534/a360534.gp.txt">PARI program</a>
%e The first terms are:
%e n a(n) a(n) aligned
%e -- ------ ------------
%e 1 2 2
%e 2 23 23
%e 3 3 3
%e 4 13 13
%e 5 113 113
%e 6 11 11
%e 7 211 211
%e 8 2111 2111
%e 9 22111 22111
%e 10 322111 322111
%e 11 3221 3221
%e 12 32213 32213
%e 13 2213 2213
%e 14 22133 22133
%e 15 622133 622133
%o (PARI) See Links section.
%Y Cf. A011557, A030456, A335043.
%K nonn,base
%O 1,1
%A _Rémy Sigrist_, Feb 10 2023