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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 (list; graph; refs; listen; history; text; internal format)
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 numbers the 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

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 !! (n-1)

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. A061672.

Sequence in context: A249334 A064158 A064702 * A305257 A318273 A061672

Adjacent sequences:  A034707 A034708 A034709 * A034711 A034712 A034713

KEYWORD

nonn,base,nice,easy

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

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Last modified July 20 11:28 EDT 2019. Contains 325180 sequences. (Running on oeis4.)