OFFSET
1,3
COMMENTS
From Derek Orr, Mar 22 2015 (Start):
The density of these numbers is roughly steady for 10^(2*k-1) < a(n) < 10^(2*k+1) for k = 1, 2, 3, ...
Examples:
k = 1: For 10 < a(n) < 1000, n/a(n) ~ 0.08127...
k = 2: For 1000 < a(n) < 10^5, n/a(n) ~ 0.008192...
k = 3: For 10^5 < a(n) < 10^7, n/a(n) ~ 0.0007753...
(End)
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
329 + (3*2*9) = 383 (a palindrome). So, 329 is in this sequence.
MATHEMATICA
Select[Range[0, 1000], PalindromeQ[#+Times@@IntegerDigits[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 08 2019 *)
PROG
(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 rev(n+DP(n))==n+DP(n)}
# Simplified by Derek Orr, Mar 22 2015
(PARI) for(n=0, 10^3, d=digits(n); D=digits(n+prod(i=1, #d, d[i])); if(Vecrev(D)==D, print1(n, ", "))) \\ Derek Orr, Mar 22 2015
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Derek Orr, Sep 26 2013
STATUS
approved