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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. 13
 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 From Michael S. Branicky, Dec 07 2020: (Start) Each digit 0-9 eventually appears.  The digit 1 appears first in a(1), 0 in a(2), 9 in a(3), 8 in a(12), 2 in a(68), 7 in a(71), 3 in a(2280), 6 in a(2283), 5 in a(2417), and 4 in a(4280). All ten digits appear in each of a(4280) through a(121000). Conjecture: a(n) contains all ten digits for n >= 4280. (End) 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 MATHEMATICA a=1; a=10; a[n_]:=a[n]=FromDigits[Flatten[IntegerDigits/@Table[a[k], {k, n-1}]][[;; n]]]-Total@Table[a[m], {m, n-1}]; Table[a[l], {l, 30}]  (* Giorgos Kalogeropoulos, May 20 2019 *) 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; d=concat(d[^1], if(n>2, digits(a)))); a} \\ M. F. Hasler, Feb 22 2018 (Python) def a(n):     alist, c, ckm1 = [1, 10], "110", 11     for k in range(3, n+1):         ck = 10*ckm1 + int(c[k-1])         ak, ckm1 = ck - ckm1, ck         c += str(ak)         alist.append(ak)     return alist[n-1] print([a(n) for n in range(1, 24)]) # Michael S. Branicky, Dec 07 2020 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 October 21 19:16 EDT 2021. Contains 348155 sequences. (Running on oeis4.)