A217657 Delete the initial digit in decimal representation of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

Offset: 0

Author

Reinhard Zumkeller, Oct 10 2012

Keywords

• nonn
• base
• look

Comments

When n - a(n)*10^[log_10 n] >= 10^[(log_10 n) - 1], where [] denotes floor, or when n < 100 and 10|n, n is the concatenation of A000030(n) and a(n) - corrected by Glen Whitney, Jul 01 2022

a(110) = 10 is the first term > 9. The sequence consists of 10 repetitions of 0 (n = 0..9), then 9 repetitions of {0, ..., 9} (n = 10..99), then 9 repetitions of {0, ..., 99} (n = 100..999), and so on. - M. F. Hasler, Oct 18 2017

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A059995 (drop final digit of n), A000030 (initial digit of n), A202262.

Programs

Haskell

a217657 n | n <= 9    = 0
          | otherwise = 10 * a217657 n' + m where (n', m) = divMod n 10

Mathematica

Array[FromDigits@ Rest@ IntegerDigits@ # &, 121, 0] (* Michael De Vlieger, Dec 22 2019 *)

PARI

apply( A217657(n)=n%10^logint(n+!n,10), [0..199]) \\ M. F. Hasler, Oct 18 2017, edited Dec 22 2019

Python

def a(n): return 0 if n < 10 else int(str(n)[1:])
print([a(n) for n in range(121)]) # Michael S. Branicky, Jul 01 2022

Formula

a(n) = 0 if n <= 9, otherwise 10*a(floor(n/10)) + n mod 10.

a(n) = n mod 10^floor(log_10(n)), a(0) = 0. - M. F. Hasler, Oct 18 2017

Extensions

Data extended to include the first terms larger than 9, by M. F. Hasler, Dec 22 2019