A249334 Numbers n for which the digital sum contains the same distinct digits as the digital product.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 99, 123, 132, 213, 231, 312, 321, 1124, 1137, 1142, 1173, 1214, 1241, 1317, 1371, 1412, 1421, 1713, 1731, 2114, 2141, 2411, 3117, 3171, 3344, 3434, 3443, 3711, 4112, 4121, 4211, 4334, 4343, 4433, 7113, 7131, 7311, 11125, 11133

Offset

1,3

Comments

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.)

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

Union of A034710 and A249335.

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

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..201 from Jaroslav Krizek).

Example

1137 is a member since 1+1+3+7 = 12 and 1*1*3*7 = 21.
3344 is in this list because 3+3+4+4=14 has the same (distinct) digits as 3*3*4*4=144.

Prog

(Magma) [n: n in [1..10^6] | Set(Intseq(&*Intseq(n))) eq Set(Intseq(&+Intseq(n)))]
(PARI) is_A249334(n)=Set(digits(sumdigits(n)))==Set(digits(prod(i=1, #n=digits(n), n[i]))) \\ M. F. Hasler, Oct 29 2014

Crossrefs

Cf. A034710, A007953, A007954, A249335.

Cf. A061672.

Sequence in context: A128290 A110002 A232709 * A338257 A064158 A064702

Adjacent sequences: A249331 A249332 A249333 * A249335 A249336 A249337

Keyword

nonn,base

Author

Jaroslav Krizek, Oct 25 2014

Status

approved