%I #15 Jan 27 2025 21:11:41
%S 0,1,2,3,4,5,6,7,8,9,11,101,181,262,343,424,686,767,848,929,1001,
%T 10001,100001,1000001,10000001,100000001,1000000001,10000000001,
%U 100000000001,1000000000001
%N Palindromes m such that m - sum_of_digits(m) is also a palindrome.
%C It is conjectured that a(n) = 10^(n-18) + 1 for all n > 20. - _Derek Orr_, Apr 05 2015
%C Palindromes in the sequence A229621.
%e 767 - (7+6+7) = 747 (another palindrome). So, 767 is in this sequence.
%t palQ[n_]:=Module[{idn=IntegerDigits[n], idn2}, idn2=IntegerDigits[n - Total[idn]]; idn==Reverse[idn]&&idn2==Reverse[idn2]]; Select[Range[0, 2 10^6], palQ] (* _Vincenzo Librandi_, Apr 06 2015 *)
%o (Python)
%o def pal(n):
%o r = ''
%o for i in str(n):
%o r = i + r
%o return r == str(n)
%o def DS(n):
%o s = 0
%o for i in str(n):
%o s += int(i)
%o return s
%o {print(n, end=', ') for n in range(10**6) if pal(n) and pal(n-DS(n))}
%o ## Simplified by _Derek Orr_, Apr 05 2015
%o (PARI) b(n)={my(d, i, r); r=vector(#digits(n-10^(#digits(n\11)))+#digits(n\11)); n=n-10^(#digits(n\11)); d=digits(n); for(i=1, #d, r[i]=d[i]; r[#r+1-i]=d[i]); sum(i=1, #r, 10^(#r-i)*r[i])} \\ Code from _David A. Corneth_ in A002113, Jun 06 2014
%o pal(n)=my(d=digits(n));Vecrev(d)==d
%o for(n=1,10^7,my(m=b(n), s=sumdigits(m));if(pal(m-s),print1(m,", "))) \\ _Derek Orr_, Apr 05 2015
%Y Cf. A229621, A002113.
%K nonn,base
%O 1,3
%A _Derek Orr_, Sep 26 2013