A299869 - OEIS

%I #14 Feb 25 2018 21:44:06

%S 6,60,594,5945,59454,594535,5945351,59453514,594535135,5945351351,

%T 59453513510,594535135104,5945351351035,59453513510351,

%U 594535135103509,5945351351035091,59453513510350914,594535135103509135,5945351351035091351,59453513510350913508,594535135103509135082,5945351351035091350820

%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) = 6.

%C The sequence starts with a(1) = 6 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="/A299869/b299869.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) ~ 0.66*10^n, a(n) ~ 0.59*10^n. See A300000 for the proof. - _M. F. Hasler_, Feb 22 2018

%e 6 + 60 = 66 which is the concatenation of 6 and 6.

%e 6 + 60 + 594 = 660 which is the concatenation of 6, 6 and 0.

%e 6 + 60 + 594 + 5945 = 6605 which is the concatenation of 6, 6, 0 and 5.

%e From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 660 - 66 = 594, a(4) = 6605 - 660 = 5945, etc. - _M. F. Hasler_, Feb 22 2018

%o (PARI) a(n,show=1,a=6,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