cp's OEIS Frontend

A034710 Positive numbers for which the sum of digits equals the product of digits.

%I A034710 #67 Feb 08 2024 07:11:18
%S A034710 1,2,3,4,5,6,7,8,9,22,123,132,213,231,312,321,1124,1142,1214,1241,
%T A034710 1412,1421,2114,2141,2411,4112,4121,4211,11125,11133,11152,11215,
%U A034710 11222,11251,11313,11331,11512,11521,12115,12122,12151,12212,12221,12511
%N A034710 Positive numbers for which the sum of digits equals the product of digits.
%C A034710 Positive numbers k such that A007953(k) = A007954(k).
%C A034710 If k is a term, the digits of k are solutions of the equation x1*x2*...*xr = x1 + x2 + ... + xr; xi are from [1..9]. Permutations of digits (x1,...,xr) are different numbers k with the same property A007953(k) = A007954(k). 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
%C A034710 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
%C A034710 There are terms of the sequence ending in any term of A052382. - _Robert Israel_, Nov 02 2014
%C A034710 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 Dougherty-Bliss_, Jun 23 2020
%H A034710 Alois P. Heinz, <a href="/A034710/b034710.txt">Table of n, a(n) for n = 1..27597</a> (first 1200 terms from T. D. Noe)
%e A034710 1124 is a term since 1 + 1 + 2 + 4 = 1*1*2*4 = 8.
%t A034710 Select[Range[12512], (Plus @@ IntegerDigits[ # ]) == (Times @@ IntegerDigits[ # ]) &] (* _Alonso del Arte_, May 16 2005 *)
%o A034710 (Haskell)
%o A034710 import Data.List (elemIndices)
%o A034710 a034710 n = a034710_list !! (n-1)
%o A034710 a034710_list = elemIndices 0 $ map (\x -> a007953 x - a007954 x) [1..]
%o A034710 -- _Reinhard Zumkeller_, Mar 19 2011
%o A034710 (Magma) [n: n in [1..10^6] | &*Intseq(n) eq &+Intseq(n)] // _Jaroslav Krizek_, Oct 25 2014
%o A034710 (PARI) is(n)=my(d=digits(n)); vecsum(d)==factorback(d) \\ _Charles R Greathouse IV_, Feb 06 2017
%Y A034710 Cf. A002473, A007953, A007954, A052382, A061672, A248794, A249334, A249335.
%Y A034710 Cf. A066306 (prime terms), A066307 (nonprimes).
%K A034710 nonn,base,nice,easy
%O A034710 1,2
%A A034710 _Erich Friedman_
%E A034710 Corrected by Larry Reeves (larryr(AT)acm.org), Jun 27 2001
%E A034710 Definition changed by _N. J. A. Sloane_ to specifically exclude 0, Sep 22 2007