

A299869


The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, and a(1) = 6.


2



6, 60, 594, 5945, 59454, 594535, 5945351, 59453514, 594535135, 5945351351, 59453513510, 594535135104, 5945351351035, 59453513510351, 594535135103509, 5945351351035091, 59453513510350914, 594535135103509135, 5945351351035091351, 59453513510350913508, 594535135103509135082, 5945351351035091350820
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OFFSET

1,1


COMMENTS

The sequence starts with a(1) = 6 and is always extended with the smallest integer not yet present in the sequence and not leading to a contradiction.


LINKS

JeanMarc Falcoz, Table of n, a(n) for n = 1..300


FORMULA

a(n) = c(n)  c(n1), where c(n) = concatenation of the first n digits, c(n) ~ 0.66*10^n, a(n) ~ 0.59*10^n. See A300000 for the proof.  M. F. Hasler, Feb 22 2018


EXAMPLE

6 + 60 = 66 which is the concatenation of 6 and 6.
6 + 60 + 594 = 660 which is the concatenation of 6, 6 and 0.
6 + 60 + 594 + 5945 = 6605 which is the concatenation of 6, 6, 0 and 5.
From n = 3 on, a(n) can be computed directly as c(n)  c(n1), cf. formula: a(3) = 660  66 = 594, a(4) = 6605  660 = 5945, etc.  M. F. Hasler, Feb 22 2018


PROG

(PARI) a(n, show=1, a=6, 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.
Cf. A299865, ..., A299872 for variants with a(1) = 2, ..., 9.
Sequence in context: A054880 A186656 A122653 * A136943 A179200 A136938
Adjacent sequences: A299866 A299867 A299868 * A299870 A299871 A299872


KEYWORD

nonn,base


AUTHOR

Eric Angelini and JeanMarc Falcoz, Feb 21 2018


STATUS

approved



