A229547 -id:A229547 - cp's OEIS frontend

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

Derek Orr, Sep 30 2013

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

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

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

Cf. A229547, A007954.

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 *)

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

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

More terms from Derek Orr, Apr 05 2015

A244541 Numbers n such that n +/- the product of digits of n are both palindromes.

Original entry on oeis.org

1, 2, 3, 4, 101, 202, 247, 252, 303, 348, 404, 505, 606, 707, 808, 843, 909, 1001, 2002, 3003, 4004, 5005, 6006, 7007, 8008, 9009, 10001, 10101, 10201, 10301, 10401, 10501, 10601, 10701, 10801, 10901, 11011, 12021, 13031, 14041, 15051, 15451, 16061, 17071, 18081, 19091, 20002

Offset: 1

Derek Orr, Jun 29 2014

			252 + 2*5*2 = 272, a palindrome, and 252 - 2*5*2 = 232, also a palindrome. Thus 252 is a member of this sequence.

Cf. A007954, A229546, A229547.

rev(n)={r="";for(i=1,#digits(n),r=concat(Str(digits(n)[i]),r));return(eval(r))}
for(n=1,10^5,dig=digits(n);p=prod(k=1,#dig,dig[k]);mi=n-p;ma=n+p;if(rev(mi)==mi&&rev(ma)==ma,print1(n,", ")))

cp's OEIS Frontend

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

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