A299871 The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, and a(1) = 8.

8, 80, 792, 7927, 79272, 792713, 7927135, 79271352, 792713513, 7927135135, 79271351350, 792713513502, 7927135135013, 79271351350135, 792713513501345, 7927135135013455, 79271351350134552, 792713513501345513, 7927135135013455135, 79271351350134551344, 792713513501345513442, 7927135135013455134424

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Feb 21 2018

Keywords

• nonn
• base

Comments

The sequence starts with a(1) = 8 and is always extended with the smallest integer not yet present in the sequence and not leading to a contradiction.

Examples

			8 + 80 = 88 which is the concatenation of 8 and 8.
8 + 80 + 792 = 880 which is the concatenation of 8, 8 and 0.
8 + 80 + 792 + 7927 = 8807 which is the concatenation of 8, 8, 0 and 7.
From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 880 - 88 = 792, a(4) = 8807 - 880 = 7927, 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=8,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) ~ 0.88*10^n, a(n) ~ 0.79*10^n. See A300000 for the proof. - M. F. Hasler, Feb 22 2018