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A061672
Smallest positive number formed by a set of digits whose product = sum of the digits.
10
1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 123, 1124, 11125, 11133, 11222, 111126, 1111127, 1111134, 11111128, 11111223, 111111129, 111111135, 1111111144, 11111111136, 11111111224, 111111112222, 1111111111137, 1111111111145, 1111111111233
OFFSET
1,2
COMMENTS
From M. F. Hasler, Oct 29 2014: (Start)
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".
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)
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..667 (terms n=1..134 from T. D. Noe).
Sean A. Irvine, Java program (github)
EXAMPLE
1124 is a term since 1 + 1 + 2 + 4 = 1*1*2*4 = 8.
PROG
(PARI) is_A061672(n)={vecsort(n=digits(n))==n && normlp(n, 1)==prod(i=1, #n, n[i])} \\ M. F. Hasler, Oct 29 2014
CROSSREFS
Sequence in context: A034710 A305257 A318273 * A272814 A322516 A132080
KEYWORD
nonn,base,easy
AUTHOR
Amarnath Murthy, Jun 26 2001
EXTENSIONS
Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 27 2001
Corrected by Franklin T. Adams-Watters, Oct 25 2006
Further corrections from T. D. Noe, Oct 12 2007
STATUS
approved