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

1,2

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

Cf. A034710, A249334.

Sequence in context: A034710 A305257 A318273 * A272814 A322516 A132080

Adjacent sequences: A061669 A061670 A061671 * A061673 A061674 A061675

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