cp's OEIS Frontend

A229761 Zeroless numbers n such that n and n - (product of digits of n) are both palindromes.

%I A229761 #31 Mar 19 2025 14:26:52
%S A229761 1,2,3,4,5,6,7,8,9,252,676,777,838,868,919,929,939,15451,15851,25152,
%T A229761 25252,25352,25452,25552,25652,25752,25852,25952,29592,36563,51415,
%U A229761 51815,52125,52225,52325,52425,52525,52625,52725,52825,52925,63536,92529,93939,97779,1455541,1545451,1558551,1594951
%N A229761 Zeroless numbers n such that n and n - (product of digits of n) are both palindromes.
%C A229761 Palindromes with nonzero digits in the sequence A229547.
%C A229761 Palindromes with an even number of digits do not appear to be in this sequence. - _Derek Orr_, Apr 05 2015
%H A229761 Chai Wah Wu, <a href="/A229761/b229761.txt">Table of n, a(n) for n = 1..10000</a>
%e A229761 929 - (9*2*9) = 767 (another palindrome). So, 929 is a member of this sequence.
%t A229761 bpQ[n_]:=DigitCount[n,10,0]==0&&AllTrue[{n,n-Times@@IntegerDigits[n]},PalindromeQ]; Select[Range[16*10^5],bpQ] (* _Harvey P. Dale_, Nov 11 2024 *)
%o A229761 (Python)
%o A229761 def DP(n):
%o A229761   p = 1
%o A229761   for i in str(n):
%o A229761     p *= int(i)
%o A229761   return p
%o A229761 def pal(n):
%o A229761   r = ''
%o A229761   for i in str(n):
%o A229761     r = i + r
%o A229761   return r == str(n)
%o A229761 {print(n, end=', ') for n in range(1, 10**6) if DP(n) and pal(n) and pal(n-DP(n))}
%o A229761 ## Simplified by _Derek Orr_, Apr 05 2015
%o A229761 (PARI) pal(n)=d=digits(n);Vecrev(d)==d
%o A229761 for(n=1,10^7,d=digits(n);p=prod(i=1,#d,d[i]);if(p&&pal(n)&&pal(n-p),print1(n,", "))) \\ _Derek Orr_, Apr 05 2015
%Y A229761 Cf. A229547, A007954.
%K A229761 nonn,easy,base
%O A229761 1,2
%A A229761 _Derek Orr_, Sep 30 2013
%E A229761 More terms from _Derek Orr_, Apr 05 2015