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.

4, 40, 396, 3963, 39636, 396357, 3963567, 39635676, 396356757, 3963567567, 39635675670, 396356756706, 3963567567057, 39635675670567, 396356756705673, 3963567567056727, 39635675670567276, 396356756705672757, 3963567567056727567, 39635675670567275672, 396356756705672756722

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Feb 21 2018

Keywords

• nonn
• base
• easy

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.

Examples

			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
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..300

Crossrefs

A300000 is the lexicographically first sequence of this type, with a(1) = 1.

Cf. A299865, ..., A299872 for variants with a(1) = 2, ..., 9.

Programs

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

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