A052246 Concatenation of integers from n down to 0.

0, 10, 210, 3210, 43210, 543210, 6543210, 76543210, 876543210, 9876543210, 109876543210, 11109876543210, 1211109876543210, 131211109876543210, 14131211109876543210, 1514131211109876543210, 161514131211109876543210, 17161514131211109876543210

Offset: 0

Author

Henry Bottomley, Feb 01 2000

Keywords

• base
• easy
• nonn
• changed

Crossrefs

Cf. A000422.

Programs

Maple

a:= proc(n) a(n):= `if`(n=0, 0, parse(cat(n, a(n-1)))) end:
seq(a(n), n=0..22);  # Alois P. Heinz, Jan 12 2021

Mathematica

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

PARI

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

Formula

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.

a(n) = A000422(n)*10.