A229184 Numbers decremented by their digit product produce a cube.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 71, 145, 167, 264, 361, 757, 1000, 1439, 1791, 2233, 3525, 3627, 3959, 4096, 4864, 4995, 6677, 8000, 8128, 8672, 9575, 10648, 14848, 23488, 24976, 25199, 25829, 26549, 27000, 27224, 35648, 39304, 43235, 50653, 53893, 64000, 74088, 79507, 91215, 93285, 94365

Offset

1,3

Comments

4 is the only zeroless number < 10^7 that is a member of this sequence and A229185 (Numbers incremented by their digit product produce a cube).

Links

Table of n, a(n) for n=1..51.

Example

167 - 1*6*7 = 125 = 5^3.

Mathematica

Select[Range[0, 100000], IntegerQ[(# - Times @@ IntegerDigits[#])^(1/3)] &] (* T. D. Noe, Sep 16 2013 *)

Prog

(Python)
def DP(n):
..p = 1
..for i in str(n):
....p *= int(i)
..return p
for n in range(10**4):
..k = 0
..P = n - DP(n)
..while P >= k**3:
....if P == k**3:
......print(n, end=', ')
......break
....k += 1
# Simplified by Derek Orr, Mar 12 2015
(PARI) for(n=0, 10^5, d=digits(n); P=n-prod(i=1, #d, d[i]); if(ispower(P, 3), print1(n, ", "))) \\ Derek Orr, Mar 12 2015

Crossrefs

Cf. A007954, A228187.

Sequence in context: A302499 A024662 A153670 * A331203 A302173 A348799

Adjacent sequences: A229181 A229182 A229183 * A229185 A229186 A229187

Keyword

nonn,easy,base

Author

Derek Orr, Sep 15 2013

Extensions

More terms and prepended a(1) = 0 from Derek Orr, Mar 12 2015

Status

approved