cp's OEIS Frontend

A249334 Numbers for which the digital sum contains the same distinct digits as the digital product.

%I A249334 #23 Sep 01 2025 11:56:21
%S A249334 0,1,2,3,4,5,6,7,8,9,22,99,123,132,213,231,312,321,1124,1137,1142,
%T A249334 1173,1214,1241,1317,1371,1412,1421,1713,1731,2114,2141,2411,3117,
%U A249334 3171,3344,3434,3443,3711,4112,4121,4211,4334,4343,4433,7113,7131,7311,11125,11133
%N A249334 Numbers for which the digital sum contains the same distinct digits as the digital product.
%C A249334 Numbers k such that A007953(k) contains the same distinct digits as A007954(k). (But either of the two may contain some digit(s) more than once.)
%C A249334 Supersequence of A034710 (positive numbers for which the sum of digits is equal to the product of digits).
%C A249334 Union of A034710 and A249335.
%C A249334 The sequence is infinite since, e.g., A002275(n) = (10^n-1)/9 is in the sequence for all n = A002275(k), k>=0; and more generally N(k,d) = A002275(n)-1+d with n = (A002275(k)-1)*d+1, k>0 and 0<d<10 (with n digits which sum to n-1+d = (10^k-1)/9*d). - _M. F. Hasler_, Oct 29 2014
%H A249334 Chai Wah Wu, <a href="/A249334/b249334.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..201 from Jaroslav Krizek).
%e A249334 1137 is a term because 1+1+3+7 = 12 and 1*1*3*7 = 21.
%e A249334 3344 is a term because 3+3+4+4=14 has the same (distinct) digits as 3*3*4*4=144.
%t A249334 Select[Range[0,12000],Union[IntegerDigits[Total[IntegerDigits[#]]]]==Union[IntegerDigits[Times@@IntegerDigits[#]]]&] (* _Harvey P. Dale_, Aug 17 2025 *)
%o A249334 (Magma) [0] cat [n: n in [1..10^6] | Set(Intseq(&*Intseq(n))) eq Set(Intseq(&+Intseq(n)))];
%o A249334 (PARI) is_A249334(n)=Set(digits(sumdigits(n)))==Set(digits(prod(i=1,#n=digits(n),n[i]))) \\ _M. F. Hasler_, Oct 29 2014
%Y A249334 Cf. A034710, A007953, A007954, A249335.
%Y A249334 Cf. A061672.
%K A249334 nonn,base,changed
%O A249334 1,3
%A A249334 _Jaroslav Krizek_, Oct 25 2014