A144777 Integers having decimal digital mean equal to zero.

18, 27, 36, 45, 54, 63, 72, 81, 90, 1089, 1098, 1179, 1188, 1197, 1269, 1278, 1287, 1296, 1359, 1368, 1377, 1386, 1395, 1449, 1458, 1467, 1476, 1485, 1494, 1539, 1548, 1557, 1566, 1575, 1584, 1593, 1629, 1638, 1647, 1656, 1665, 1674, 1683, 1692, 1719

Offset: 1

Author

Reikku Kulon, Sep 21 2008

Keywords

• base
• easy
• nonn

Comments

Define the digital mean of n in base b, dm(b, n), to be (Sum_{i=1..d} 2*d_i - (b-1)) / (2*d), where d is the number of digits in the base b representation of n and d_i the individual digits.

a(n) is the subset of multiples of nine for which dm(10, n) = 0; that is, two times the sum of the digits is equal to nine times the number of digits.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A008591.

Programs

Mathematica

Select[Range[200]*9, 2*DigitSum[#] == 9*IntegerLength[#] &] (* Paolo Xausa, May 17 2024 *)