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Concatenation of integers from n down to 0.
1

%I #10 Jan 12 2021 08:39:55

%S 0,10,210,3210,43210,543210,6543210,76543210,876543210,9876543210,

%T 109876543210,11109876543210,1211109876543210,131211109876543210,

%U 14131211109876543210,1514131211109876543210,161514131211109876543210,17161514131211109876543210

%N Concatenation of integers from n down to 0.

%F a(0)=0, a(n) = n*10^len(a(n-1)) + a(n-1), where len(k) = number of digits in k and len(0)=1; = A000422*10.

%p a:= proc(n) a(n):= `if`(n=0, 0, parse(cat(n, a(n-1)))) end:

%p seq(a(n), n=0..22); # _Alois P. Heinz_, Jan 12 2021

%t nn=20;With[{c=Range[nn,0,-1]},Table[FromDigits[Flatten[ IntegerDigits/@ Take[ c,-n]]],{n,nn}]] (* _Harvey P. Dale_, Feb 01 2013 *)

%o (PARI) /* computation by definition: */

%o a(n)=if(n==0, 0, eval(Str(n, a(n-1)))); \\ Joerg Arndt, Sep 14 2014

%Y Cf. A000422.

%K base,easy,nonn

%O 0,2

%A _Henry Bottomley_, Feb 01 2000