cp's OEIS Frontend

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

%I A084019 #24 Jun 14 2024 01:49:09
%S A084019 9,8,7,6,5,4,3,2,1,0,88,77,66,55,44,33,22,11,0,898,888,878,868,858,
%T A084019 848,838,828,818,808,797,787,777,767,757,747,737,727,717,707,696,686,
%U A084019 676,666,656,646,636,626,616
%N A084019 a(n) = 9's complement of n-th palindrome (A002113).
%C A084019 Leading zeros in the 9's complement are omitted.
%C A084019 For palindromes of the form 10^k-1 the corresponding entry is zero. Apart from this the entries are distinct.
%H A084019 Indranil Ghosh, <a href="/A084019/b084019.txt">Table of n, a(n) for n = 1..25000</a>
%e A084019 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
%o A084019 (Python)
%o A084019 # Program for generating the b-file
%o A084019 def a(n):
%o A084019     return 10**len(str(n))-n-1
%o A084019 i=0
%o A084019 j=1
%o A084019 while j<=250:
%o A084019     if i==int(str(i)[::-1]):
%o A084019         print(str(j)+" "+str(a(i)))
%o A084019         j+=1
%o A084019     i+=1 # _Indranil Ghosh_, Jan 30 2017
%o A084019 (Python)
%o A084019 def A084019(n):
%o A084019     if n == 1: return 9
%o A084019     y = 10*(x:=10**(len(str(n>>1))-1))
%o A084019     if n<x+y:
%o A084019         c = n-x
%o A084019         c = 10**len(str(c))-1-c
%o A084019         return c*x+int(str(c)[-2::-1]or 0)
%o A084019     else:
%o A084019         c = n-y
%o A084019         c = 10**len(str(c))-1-c
%o A084019         return c*y+int(str(c)[-1::-1]or 0) # _Chai Wah Wu_, Jun 13 2024
%Y A084019 Cf. A002113, A061601, A084020.
%K A084019 base,easy,nonn
%O A084019 1,1
%A A084019 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 23 2003