A226468 Numbers in which each digit equals the sum (mod 10) of the other digits.

11, 22, 33, 44, 55, 66, 77, 88, 99, 505, 550, 5005, 5050, 5500, 5555, 50005, 50050, 50500, 50555, 55000, 55055, 55505, 55550, 500005, 500050, 500500, 500555, 505000, 505055, 505505, 505550, 550000, 550055, 550505, 550550, 555005, 555050, 555500, 555555, 1111116

Offset: 1

Author

Michel Lagneau, Jun 08 2013

Keywords

• nonn
• base

Comments

The primitive terms in this sequence are 11, 22, 33, 44, 55, 66, 77, 88, 99, 505, 5005, 5555, 50005, 50555, 500005, 500555, 555555, 1111116, 1111666, 1166666, 2222222, 2222277, ...; the other terms are built from the permutations of the digits of these numbers.

We find the following subsequences:

505, 5005, 50005, 500005, ..., 5000000005;

55, 5555, 555555, 55555555, ..., 5555555555.

Examples

			505 is in the sequence because the digits 5,0,5 satisfy
  5 = (0 + 5) mod 10;
  0 = (5 + 5) mod 10;
  5 = (5 + 0) mod 10.
		

Crossrefs

Cf. A007953, A053837.

Programs

Mathematica

Select[Range[10^5], IntegerDigits[#] == Mod[Total[IntegerDigits[#]] - IntegerDigits[#], 10] &]

Extensions

Edited by Jon E. Schoenfield, Sep 09 2017