OFFSET
1,1
COMMENTS
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.
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..300
FORMULA
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
EXAMPLE
6 + 60 = 66 which is the concatenation of 6 and 6.
6 + 60 + 594 = 660 which is the concatenation of 6, 6 and 0.
6 + 60 + 594 + 5945 = 6605 which is the concatenation of 6, 6, 0 and 5.
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
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Feb 21 2018
STATUS
approved