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

1, 2, 3, 4, 5, 6, 7, 8, 9, 252, 676, 777, 838, 868, 919, 929, 939, 15451, 15851, 25152, 25252, 25352, 25452, 25552, 25652, 25752, 25852, 25952, 29592, 36563, 51415, 51815, 52125, 52225, 52325, 52425, 52525, 52625, 52725, 52825, 52925, 63536, 92529, 93939, 97779, 1455541, 1545451, 1558551, 1594951

Offset: 1

Author

Derek Orr, Sep 30 2013

Keywords

• nonn
• easy
• base

Comments

Palindromes with nonzero digits in the sequence A229547.

Palindromes with an even number of digits do not appear to be in this sequence. - Derek Orr, Apr 05 2015

Examples

			929 - (9*2*9) = 767 (another palindrome). So, 929 is a member of this sequence.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A229547, A007954.

Programs

Mathematica

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 *)

PARI

pal(n)=d=digits(n);Vecrev(d)==d
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

Python

def DP(n):
  p = 1
  for i in str(n):
    p *= int(i)
  return p
def pal(n):
  r = ''
  for i in str(n):
    r = i + r
  return r == str(n)
{print(n, end=', ') for n in range(1, 10**6) if DP(n) and pal(n) and pal(n-DP(n))}
## Simplified by Derek Orr, Apr 05 2015

Extensions

More terms from Derek Orr, Apr 05 2015