A229804 Zeroless numbers n such that n and n*product_of_digits(n) are both palindromes.

1, 2, 3, 11, 22, 77, 111, 121, 131, 212, 464, 1111, 1221, 2112, 11111, 11211, 11311, 12121, 21112, 22622, 111111, 112211, 121121, 211112, 1111111, 1112111, 1113111, 1121211, 1211121, 2111112, 2223222, 4213124, 11111111, 11122111, 11211211, 12111121, 21111112

Offset

1,2

Comments

Palindromes in the sequence A229550.

Links

Giovanni Resta, Table of n, a(n) for n = 1..200

Example

77*(7*7) = 343*11 = 3773 (another palindrome). So 77 is a member of this sequence.
464*(4*6*4) = 44544 (another palindrome). So, 464 is a member of this sequence.

Mathematica

Select[Range[21111112], DigitCount[#, 10, 0]==0&&AllTrue[{#, #*Times@@IntegerDigits[#]}, PalindromeQ]&] (* Harvey P. Dale, Apr 27 2025 *)

Prog

(Python)
def pal(n):
  r = ''
  for i in str(n):
    r = i + r
  return r == str(n)
def DP(n):
  p = 1
  for i in str(n):
    p *= int(i)
  return p
{print(n, end=', ') for n in range(1, 10**6) if DP(n)*pal(n)*pal(n*DP(n))}
## Simplified by Derek Orr, Apr 05 2015
(PARI) pal(n)=d=digits(n); Vecrev(d)==d
for(n=1, 10^8, 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. A229550, A007954.

Sequence in context: A128921 A118595 A229549 * A241096 A057135 A229805

Adjacent sequences: A229801 A229802 A229803 * A229805 A229806 A229807

Keyword

nonn,easy,base

Author

Derek Orr, Sep 29 2013

Status

approved