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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.
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%I #14 Oct 30 2018 04:37:33

%S 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,

%T 73,79,83,89,97,10,12,27,39,14,49,15,51,57,16,63,18,81,91,93,99,21,22,

%U 33,24,25,26,69,77,28,30,34,35,36,38,40,42,44,45,46,48,87

%N 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.

%C This sequence is a variant of A321043.

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

%C Prime numbers appear in increasing order.

%H Rémy Sigrist, <a href="/A321128/b321128.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A321128/a321128.png">Colored scatterplot of the first 100000 terms</a>

%H Rémy Sigrist, <a href="/A321128/a321128_1.png">Scatterplot of the first 100000 terms of the analog for the Euler totient function (A000010)</a>

%H Rémy Sigrist, <a href="/A321128/a321128.gp.txt">PARI program for A321128</a>

%e The first terms, alongside the corresponding prime numbers, are:

%e n a(n) Prime

%e -- ---- -----

%e 1 2 2

%e 2 3 3

%e 3 5 5

%e 4 7 7

%e 5 1 11

%e 6 9 19

%e 7 4 41

%e 8 6 61

%e 9 8 83

%e 10 0 101

%e 11 11 11

%e 12 13 13

%e ...

%e 30 89 89

%e 31 97 97

%e 32 10 101

%e 33 12 127

%e 34 27 127

%e 35 39 139

%e 36 14 149

%e 37 49 149

%o (PARI) See Links section.

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

%K nonn,base,look

%O 1,1

%A _Rémy Sigrist_, Oct 27 2018