A229547 Numbers n such that n - product_of_digits(n) is a palindrome.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 29, 34, 46, 57, 61, 78, 82, 93, 101, 129, 143, 187, 202, 218, 226, 244, 247, 252, 269, 294, 297, 303, 319, 336, 348, 357, 361, 364, 386, 404, 412, 419, 437, 453, 462, 488, 505, 514, 519, 524, 534, 539, 544, 554, 564, 574, 584, 594, 597, 606, 613, 615, 617, 619, 625, 635, 638, 645, 655, 663

Offset: 1

Author

Derek Orr, Sep 26 2013

Keywords

• nonn
• base
• easy

Examples

			143 - (1*4*3) = 131 (a palindrome). So, 143 is a member of the sequence.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070565.

Programs

Mathematica

f[n_] := Block[{d = n - Times @@ IntegerDigits@ n}, d == FromDigits@ Reverse[IntegerDigits@ d]]; Select[Range[0, 1000], f] (* Michael De Vlieger, Mar 12 2015 *)

PARI

for(n=0,10^3,d=digits(n);p=prod(i=1,#d,d[i]);if(Vecrev(digits(n-p))==digits(n-p),print1(n,", "))) \\ Derek Orr, Mar 12 2015

Python

def rev(n):
    return int(''.join(reversed(str(n))))
def DP(n):
    p = 1
    for i in str(n):
        p *= int(i)
    return p
{print(n, end=', ') for n in range(10**3) if n-DP(n)==rev(n-DP(n))}
# Simplified by Derek Orr, Mar 12 2015

Extensions

More terms from Derek Orr, Mar 12 2015