

A299865


The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, and a(1) = 2.


9



2, 20, 198, 1981, 19818, 198179, 1981783, 19817838, 198178379, 1981783783, 19817837830, 198178378308, 1981783783079, 19817837830783, 198178378307837, 1981783783078363, 19817837830783638, 198178378307836379, 1981783783078363783, 19817837830783637836, 198178378307836378362, 1981783783078363783612
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OFFSET

1,1


COMMENTS

The sequence starts with a(1) = 2 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) ~ 0.22*10^n, a(n) ~ 0.198*10^n. See A300000 for the proof.  M. F. Hasler, Feb 22 2018


EXAMPLE

2 + 20 = 22 which is the concatenation of 2 and 2.
2 + 20 + 198 = 220 which is the concatenation of 2, 2 and 0.
2 + 20 + 198 + 1981 = 2201 which is the concatenation of 2, 2, 0 and 1.


PROG

(PARI) a(n, show=1, a=2, 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

A300000 is the lexicographically first sequence of this type, with a(1) = 1.
Cf. A299866, ..., A299872 for variants with a(1) = 3, ..., 9.
Sequence in context: A171076 A287999 A001078 * A001253 A303462 A085586
Adjacent sequences: A299862 A299863 A299864 * A299866 A299867 A299868


KEYWORD

nonn,base


AUTHOR

Eric Angelini and JeanMarc Falcoz, Feb 21 2018


STATUS

approved



