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%I #14 Feb 25 2018 21:44:06
%S 7,70,693,6936,69363,693624,6936243,69362433,693624324,6936243243,
%T 69362432430,693624324303,6936243243024,69362432430243,
%U 693624324302427,6936243243024273,69362432430242733,693624324302427324,6936243243024273243,69362432430242732426,693624324302427324262,6936243243024273242622
%N The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, and a(1) = 7.
%C The sequence starts with a(1) = 7 and is always extended with the smallest integer not yet present in the sequence and not leading to a contradiction.
%H Jean-Marc Falcoz, <a href="/A299870/b299870.txt">Table of n, a(n) for n = 1..300</a>
%F a(n) = c(n) - c(n-1), where c(n) = concatenation of the first n digits, c(n) ~ 0.77*10^n, a(n) ~ 0.69*10^n. See A300000 for the proof. - _M. F. Hasler_, Feb 22 2018
%e 7 + 70 = 77 which is the concatenation of 7 and 7.
%e 7 + 70 + 693 = 770 which is the concatenation of 7, 7 and 0.
%e 7 + 70 + 693 + 6936 = 7706 which is the concatenation of 7, 7, 0 and 6.
%e From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 770 - 77 = 693, a(4) = 7706 - 770 = 6936, etc. - _M. F. Hasler_, Feb 22 2018
%o (PARI) a(n,show=1,a=7,c=a,d=[a])={for(n=2,n,show&&print1(a",");a=-c+c=c*10+d[1];d=concat(d[^1],if(n>2,digits(a))));a} \\ _M. F. Hasler_, Feb 22 2018
%Y A300000 is the lexicographically first sequence of this type, with a(1) = 1.
%Y Cf. A299865, ..., A299872 for variants with a(1) = 2, ..., 9.
%K nonn,base
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 21 2018
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