

A034710


Positive numbers for which the sum of digits equals the product of digits.


29



1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 123, 132, 213, 231, 312, 321, 1124, 1142, 1214, 1241, 1412, 1421, 2114, 2141, 2411, 4112, 4121, 4211, 11125, 11133, 11152, 11215, 11222, 11251, 11313, 11331, 11512, 11521, 12115, 12122, 12151, 12212, 12221, 12511
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OFFSET

1,2


COMMENTS

Positive numbers n such that A007953(n) = A007954(n).
If n is a member, the digits of n are solutions of the equation x1*x2*...*xr = x1 + x2 + ... + xr; xi are from [1...9]. Permutations of digits (x1,...,xr) are different numbers n with the same property S(n)=PI(n). For example: x1*x2 = x1 + x2; this equation has only 1 solution, (2,2), which gives the number 22. x1*x2*x3 = x1 + x2 + x3 has a solution (1,2,3), so the numbers 123, 132, 213, 231, 312, 321 have the property.  Ctibor O. Zizka, Mar 04 2008
Subsequence of A249334 (numbers for which the digital sum contains the same distinct digits as the digital product). With {0}, complement of A249335 with respect to A249334. Sequence of corresponding values of A007953(a(n)) = A007954(a(n)): 1, 2, 3, 4, 5, 6, 7, 8, 9, 4, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, ... contains only numbers from A002473. See A248794.  Jaroslav Krizek, Oct 25 2014
There are members of the sequence ending in any member of A052382.  Robert Israel, Nov 02 2014
The number of digits which are not 1 in a(n) is O(log log a(n)) and tends to infinity as a(n) does.  Robert DoughertyBliss, Jun 23 2020


LINKS

T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 1..27597 (first 1200 terms from T. D. Noe)


EXAMPLE

1124 is a member since 1 + 1 + 2 + 4 = 1*1*2*4 = 8.


MAPLE

select(n>convert(convert(n, base, 10), `+`)=convert(convert(n, base, 10), `*`), [$1..12511]); # Paolo P. Lava, Apr 18 2018


MATHEMATICA

Select[Range[12512], (Plus @@ IntegerDigits[ # ]) == (Times @@ IntegerDigits[ # ]) &] (Alonso del Arte, May 16 2005)


PROG

(Haskell)
import Data.List (elemIndices)
a034710 n = a034710_list !! (n1)
a034710_list = elemIndices 0 $ map (\x > a007953 x  a007954 x) [1..]
 Reinhard Zumkeller, Mar 19 2011
(MAGMA) [n: n in [1..10^6]  &*Intseq(n) eq &+Intseq(n)] // Jaroslav Krizek, Oct 25 2014
(PARI) is(n)=my(d=digits(n)); vecsum(d)==factorback(d) \\ Charles R Greathouse IV, Feb 06 2017


CROSSREFS

Cf. A002473, A007953, A007954, A052382, A061672, A248794, A249334, A249335.
Sequence in context: A249334 A064158 A064702 * A305257 A318273 A061672
Adjacent sequences: A034707 A034708 A034709 * A034711 A034712 A034713


KEYWORD

nonn,base,nice,easy,changed


AUTHOR

Erich Friedman


EXTENSIONS

Corrected by Larry Reeves (larryr(AT)acm.org), Jun 27 2001
Definition changed by N. J. A. Sloane to specifically exclude 0, Sep 22 2007


STATUS

approved



