A299866 The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, a(1) = 3.

3, 30, 297, 2972, 29727, 297268, 2972675, 29726757, 297267568, 2972675675, 29726756750, 297267567507, 2972675675068, 29726756750675, 297267567506755, 2972675675067545, 29726756750675457, 297267567506754568, 2972675675067545675, 29726756750675456754, 297267567506754567542

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Feb 21 2018

Keywords

• nonn
• base
• easy

Comments

The sequence starts with a(1) = 3 and is always extended with the smallest integer not yet present in the sequence and not leading to a contradiction.

Examples

			3 + 30 = 33 which is the concatenation of 3 and 3.
3 + 30 + 297 = 330 which is the concatenation of 3, 3 and 0.
3 + 30 + 297 + 2972 = 3302 which is the concatenation of 3, 3, 0 and 2.
From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 330 - 33 = 297, a(4) = 3302 - 330 = 2972, 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=3,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) ~ 0.33*10^n, a(n) ~ 0.297*10^n. See A300000 for the proof. - M. F. Hasler, Feb 22 2018