%I #18 Mar 04 2018 19:47:38
%S 3,30,297,2972,29727,297268,2972675,29726757,297267568,2972675675,
%T 29726756750,297267567507,2972675675068,29726756750675,
%U 297267567506755,2972675675067545,29726756750675457,297267567506754568,2972675675067545675,29726756750675456754,297267567506754567542
%N The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, a(1) = 3.
%C The sequence starts with a(1) = 3 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="/A299866/b299866.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) ~ 0.33*10^n, a(n) ~ 0.297*10^n. See A300000 for the proof. - _M. F. Hasler_, Feb 22 2018
%e 3 + 30 = 33 which is the concatenation of 3 and 3.
%e 3 + 30 + 297 = 330 which is the concatenation of 3, 3 and 0.
%e 3 + 30 + 297 + 2972 = 3302 which is the concatenation of 3, 3, 0 and 2.
%e From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 330 - 33 = 297, a(4) = 3302 - 330 = 2972, etc. - _M. F. Hasler_, Feb 22 2018
%o (PARI) a(n,show=1,a=3,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,easy
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 21 2018
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