login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

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

FORMULA

a(n) = c(n) - c(n-1), 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(n-1), 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 Jean-Marc Falcoz, Feb 21 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 30 04:28 EDT 2021. Contains 346348 sequences. (Running on oeis4.)