A249334 Numbers 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

Author

Jaroslav Krizek, Oct 25 2014

Keywords

• nonn
• base
• changed

Comments

Numbers k such that A007953(k) contains the same distinct digits as A007954(k). (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 0M. F. Hasler, Oct 29 2014

Examples

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

Links

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

Crossrefs

Cf. A034710, A007953, A007954, A249335.

Cf. A061672.

Programs

Magma

[0] cat [n: n in [1..10^6] | Set(Intseq(&*Intseq(n))) eq Set(Intseq(&+Intseq(n)))];

Mathematica

Select[Range[0,12000],Union[IntegerDigits[Total[IntegerDigits[#]]]]==Union[IntegerDigits[Times@@IntegerDigits[#]]]&] (* Harvey P. Dale, Aug 17 2025 *)

PARI

is_A249334(n)=Set(digits(sumdigits(n)))==Set(digits(prod(i=1,#n=digits(n),n[i]))) \\ M. F. Hasler, Oct 29 2014