cp's OEIS Frontend

A061672 Smallest positive number formed by a set of digits whose product = sum of the digits.

%I A061672 #24 Feb 27 2023 17:03:44
%S A061672 1,2,3,4,5,6,7,8,9,22,123,1124,11125,11133,11222,111126,1111127,
%T A061672 1111134,11111128,11111223,111111129,111111135,1111111144,11111111136,
%U A061672 11111111224,111111112222,1111111111137,1111111111145,1111111111233
%N A061672 Smallest positive number formed by a set of digits whose product = sum of the digits.
%C A061672 From _M. F. Hasler_, Oct 29 2014: (Start)
%C A061672 This is the subsequence of terms of A034710 with digits in nondecreasing order, which is meant by "smallest": For example, 132 also has sum of digits = product of digits, but is already "represented" by 123. The word "set" in the definition actually means "multiset".
%C A061672 The sequence is infinite: for any number N whose digits form a nondecreasing sequence whose sum of digits S is not larger than the product of digits P (i.e., N in A062998), a term of the sequence is obtained by prefixing N with P-S digits '1'. (End)
%H A061672 Chai Wah Wu, <a href="/A061672/b061672.txt">Table of n, a(n) for n = 1..667</a> (terms n=1..134 from T. D. Noe).
%H A061672 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a061/A061672.java">Java program</a> (github)
%e A061672 1124 is a term since 1 + 1 + 2 + 4 = 1*1*2*4 = 8.
%o A061672 (PARI) is_A061672(n)={vecsort(n=digits(n))==n && normlp(n,1)==prod(i=1,#n,n[i])} \\ _M. F. Hasler_, Oct 29 2014
%Y A061672 Cf. A034710, A249334.
%K A061672 nonn,base,easy
%O A061672 1,2
%A A061672 _Amarnath Murthy_, Jun 26 2001
%E A061672 Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 27 2001
%E A061672 Corrected by _Franklin T. Adams-Watters_, Oct 25 2006
%E A061672 Further corrections from _T. D. Noe_, Oct 12 2007