A299870 The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, and a(1) = 7.

7, 70, 693, 6936, 69363, 693624, 6936243, 69362433, 693624324, 6936243243, 69362432430, 693624324303, 6936243243024, 69362432430243, 693624324302427, 6936243243024273, 69362432430242733, 693624324302427324, 6936243243024273243, 69362432430242732426, 693624324302427324262, 6936243243024273242622

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Feb 21 2018

Keywords

• nonn
• base

Comments

The sequence starts with a(1) = 7 and is always extended with the smallest integer not yet present in the sequence and not leading to a contradiction.

Examples

			7 + 70 = 77 which is the concatenation of 7 and 7.
7 + 70 + 693 = 770 which is the concatenation of 7, 7 and 0.
7 + 70 + 693 + 6936 = 7706 which is the concatenation of 7, 7, 0 and 6.
From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 770 - 77 = 693, a(4) = 7706 - 770 = 6936, 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=7,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) ~ 0.77*10^n, a(n) ~ 0.69*10^n. See A300000 for the proof. - M. F. Hasler, Feb 22 2018