A084019 a(n) = 9's complement of n-th palindrome (A002113).

9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 88, 77, 66, 55, 44, 33, 22, 11, 0, 898, 888, 878, 868, 858, 848, 838, 828, 818, 808, 797, 787, 777, 767, 757, 747, 737, 727, 717, 707, 696, 686, 676, 666, 656, 646, 636, 626, 616

Offset

1,1

Comments

Leading zeros in the 9's complement are omitted.

For palindromes of the form 10^k-1 the corresponding entry is zero. Apart from this the entries are distinct.

Links

Indranil Ghosh, Table of n, a(n) for n = 1..25000

Example

The 20th palindromic number A002113(20) is 101 having 9's complement 898 (999 - 101 = 898). So a(20) = 898. - Indranil Ghosh, Jan 30 2017

Prog

(Python)
# Program for generating the b-file
def a(n):
    return 10**len(str(n))-n-1
i=0
j=1
while j<=250:
    if i==int(str(i)[::-1]):
        print(str(j)+" "+str(a(i)))
        j+=1
    i+=1 # Indranil Ghosh, Jan 30 2017
(Python)
def A084019(n):
    if n == 1: return 9
    y = 10*(x:=10**(len(str(n>>1))-1))
    if n<x+y:
        c = n-x
        c = 10**len(str(c))-1-c
        return c*x+int(str(c)[-2::-1]or 0)
    else:
        c = n-y
        c = 10**len(str(c))-1-c
        return c*y+int(str(c)[-1::-1]or 0) # Chai Wah Wu, Jun 13 2024

Crossrefs

Cf. A002113, A061601, A084020.

Sequence in context: A023451 A109910 A307340 * A061601 A098756 A267193

Adjacent sequences: A084016 A084017 A084018 * A084020 A084021 A084022

Keyword

base,easy,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 23 2003

Status

approved