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%I #16 Feb 25 2018 21:44:06
%S 5,50,495,4954,49545,495446,4954459,49544595,495445946,4954459459,
%T 49544594590,495445945905,4954459459046,49544594590459,
%U 495445945904591,4954459459045909,49544594590459095,495445945904590946,4954459459045909459,49544594590459094590,495445945904590945902,4954459459045909459018
%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) = 5.
%C The sequence starts with a(1) = 5 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="/A299868/b299868.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) ~ 0.55*10^n, a(n) ~ 0.495*10^n. See A300000 for the proof. - _M. F. Hasler_, Feb 22 2018
%e 5 + 50 = 55 which is the concatenation of 5 and 5.
%e 5 + 50 + 495 = 550 which is the concatenation of 5, 5 and 0.
%e 5 + 50 + 495 + 4954 = 5504 which is the concatenation of 5, 5, 0 and 4.
%e From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 550 - 55 = 495, a(4) = 5504 - 550 = 4954, etc. - _M. F. Hasler_, Feb 22 2018
%o (PARI) a(n,show=1,a=5,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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