|
|
A299867
|
|
The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, and a(1) = 4.
|
|
2
|
|
|
4, 40, 396, 3963, 39636, 396357, 3963567, 39635676, 396356757, 3963567567, 39635675670, 396356756706, 3963567567057, 39635675670567, 396356756705673, 3963567567056727, 39635675670567276, 396356756705672757, 3963567567056727567, 39635675670567275672, 396356756705672756722
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The sequence starts with a(1) = 4 and is always extended with the smallest integer not yet present in the sequence and not leading to a contradiction.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = c(n) - c(n-1), where c(n) = concatenation of the first n digits, c(n) ~ 0.44*10^n, a(n) ~ 0.396*10^n. See A300000 for the proof. - M. F. Hasler, Feb 22 2018
|
|
EXAMPLE
|
4 + 40 = 44 which is the concatenation of 4 and 4.
4 + 40 + 396 = 440 which is the concatenation of 4, 4, and 0.
4 + 40 + 396 + 3963 = 4403 which is the concatenation of 4, 4, 0 and 3.
From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 440 - 4 = 396, a(4) = 4403 - 440 = 3963, etc. - M. F. Hasler, Feb 22 2018
|
|
PROG
|
(PARI) a(n, show=1, a=4, 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
|
A300000 is the lexicographically first sequence of this type, with a(1) = 1.
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|