A147882 Positive integers k that are balanced, meaning that if k has d digits, then its initial ceiling(d/2) digits have the same sum as its last ceiling(d/2) digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494

Offset: 1

Author

Jason Tarver (scottarver(AT)gmail.com), Nov 17 2008

Keywords

• nonn
• base

Comments

Differs from A110751 in cases like n=1010, 1089, 1102, 1120, 1203, 1212, 1230, etc. - R. J. Mathar, Dec 13 2008

Examples

			From _David A. Corneth_, Sep 28 2023: (Start)
353 is a term as it has k = 3 digits and so we see that the sum of the first ceiling(k/2) = ceiling(3/2) = 2 and the last ceiling(k/2) = ceiling(3/2) = 2 are equal and indeed 3 + 5 = 5 + 3.
13922 is a term as it has k = 5 digits and so we see that the sum of the first ceiling(k/2) = ceiling(5/2) = 2 and the last ceiling(k/2) = ceiling(5/2) = 2 are equal and indeed 1 + 3 + 9 = 9 + 2 + 2. (End)
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 6649 terms from Jason Tarver)
• Project Euler, Problem 217: Balanced Numbers.

Crossrefs

Cf. A002113, A110751.

Programs

PARI

is(n) = {my(d = digits(n), qdp1 = #d + 1); sum(i = 1, #d\2, d[i]-d[qdp1 - i]) == 0} \\ David A. Corneth, Sep 28 2023

Extensions

Definition clarified by N. J. A. Sloane, Oct 06 2023