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

1,2

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

Links

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A229547, A007954.

Sequence in context: A029966 A219324 A085134 * A004882 A306853 A308110

Adjacent sequences: A229758 A229759 A229760 * A229762 A229763 A229764

Keyword

nonn,easy,base

Author

Derek Orr, Sep 30 2013

Extensions

More terms from Derek Orr, Apr 05 2015

Status

approved