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A299871 The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, and a(1) = 8. 3

%I #13 Feb 25 2018 21:44:06

%S 8,80,792,7927,79272,792713,7927135,79271352,792713513,7927135135,

%T 79271351350,792713513502,7927135135013,79271351350135,

%U 792713513501345,7927135135013455,79271351350134552,792713513501345513,7927135135013455135,79271351350134551344,792713513501345513442,7927135135013455134424

%N The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, and a(1) = 8.

%C The sequence starts with a(1) = 8 and is always extended with the smallest integer not yet present in the sequence and not leading to a contradiction.

%H Jean-Marc Falcoz, <a href="/A299871/b299871.txt">Table of n, a(n) for n = 1..300</a>

%F a(n) = c(n) - c(n-1), where c(n) = concatenation of the first n digits, c(n) ~ 0.88*10^n, a(n) ~ 0.79*10^n. See A300000 for the proof. - _M. F. Hasler_, Feb 22 2018

%e 8 + 80 = 88 which is the concatenation of 8 and 8.

%e 8 + 80 + 792 = 880 which is the concatenation of 8, 8 and 0.

%e 8 + 80 + 792 + 7927 = 8807 which is the concatenation of 8, 8, 0 and 7.

%e From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 880 - 88 = 792, a(4) = 8807 - 880 = 7927, etc. - _M. F. Hasler_, Feb 22 2018

%o (PARI) a(n,show=1,a=8,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

%Y A300000 is the lexicographically first sequence of this type, with a(1) = 1.

%Y Cf. A299865, ..., A299872 for variants with a(1) = 2, ..., 9.

%K nonn,base

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 21 2018

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)