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

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

Author

Amarnath Murthy, Jun 26 2001

Keywords

• nonn
• base
• easy

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)

Examples

			1124 is a term since 1 + 1 + 2 + 4 = 1*1*2*4 = 8.
		

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)

Crossrefs

Cf. A034710, A249334.

Programs

PARI

is_A061672(n)={vecsort(n=digits(n))==n && normlp(n,1)==prod(i=1,#n,n[i])} \\ M. F. Hasler, Oct 29 2014

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