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A300000 The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, with a(1) = 1. 11
1, 10, 99, 999, 9990, 99900, 999000, 9990000, 99900000, 999000000, 9990000000, 99899999991, 998999999919, 9989999999190, 99899999991900, 998999999918991, 9989999999189910, 99899999991899109, 998999999918991090, 9989999999189910900, 99899999991899108991, 998999999918991089910, 9989999999189910899100 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

By definition, Sum_{k=1..n} a(k) = c(n) = concatenation of the first n digits of the sequence, therefore a(n) = c(n) - c(n-1). For n > 2, this defines a(n) recursively, without the need for solving an implicit equation, as the definition might suggest. - M. F. Hasler, Feb 22 2018

LINKS

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

FORMULA

a(n) = c(n) - c(n-1), where c(n) is the concatenation of the first n digits. c(n) ~ 1.1*10^(n-1), and a(n) ~ 0.999*10^(n-1). - M. F. Hasler, Feb 22 2018

EXAMPLE

1 + 10 = 11 which is the concatenation of 1 and 1.

1 + 10 + 99 = 110 which is the concatenation of 1, 1 and 0.

1 + 10 + 99 + 999 = 1109 which is the concatenation of 1, 1, 0 and 9.

Otherwise said:

a(3) = concat(1,1,0) - (1 + 10) = 110 - 11 = 99,

a(4) = concat(1,1,0,9) - (11 + 99) = 1109 - 110 = 999,

a(5) = concat(1,1,0,9,9) - 1109 = 11099 - 1109 = 9990,

a(6) = concat(1,1,0,9,9,9) - 11099 = 99900, etc. - M. F. Hasler, Feb 22 2018

PROG

(PARI) a(n, show=1, a=1, c=a, d=[c])={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

A299865, A299866, A299867, A299868, A299869, A299870, A299871 and A299872 show the same type of sequence but with a different start.

The partial sums (the sequence c(n) mentioned in the Comments) is A299301.

Sequence in context: A179555 A105694 A179557 * A213454 A000456 A138365

Adjacent sequences:  A299997 A299998 A299999 * A300001 A300002 A300003

KEYWORD

nonn,base,nice,easy

AUTHOR

Eric Angelini, Feb 10 2018

STATUS

approved

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Last modified November 15 14:23 EST 2018. Contains 317239 sequences. (Running on oeis4.)