A249334 - OEIS

%I #14 Sep 08 2022 08:46:10

%S 0,1,2,3,4,5,6,7,8,9,22,99,123,132,213,231,312,321,1124,1137,1142,

%T 1173,1214,1241,1317,1371,1412,1421,1713,1731,2114,2141,2411,3117,

%U 3171,3344,3434,3443,3711,4112,4121,4211,4334,4343,4433,7113,7131,7311,11125,11133

%N Numbers n for which the digital sum contains the same distinct digits as the digital product.

%C Numbers n such that A007953(n) contains the same distinct digits as A007954(n). (But either of the two may contain some digit(s) more than once.)

%C Supersequence of A034710 (positive numbers for which the sum of digits is equal to the product of digits).

%C Union of A034710 and A249335.

%C 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 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 1137 is a member since 1+1+3+7 = 12 and 1*1*3*7 = 21.

%e 3344 is in this list because 3+3+4+4=14 has the same (distinct) digits as 3*3*4*4=144.

%o (Magma) [n: n in [1..10^6] | Set(Intseq(&*Intseq(n))) eq Set(Intseq(&+Intseq(n)))]

%o (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 Cf. A034710, A007953, A007954, A249335.

%Y Cf. A061672.

%K nonn,base

%O 1,3

%A _Jaroslav Krizek_, Oct 25 2014