A316492 Numbers k such that the average digit in the concatenation of the numbers from 1 through k is an integer.

1, 3, 5, 7, 9, 122, 576, 1422, 1876, 4122, 4576

Offset: 1

Author

Jon E. Schoenfield, Aug 11 2018

Keywords

• nonn
• base
• fini
• full

Comments

Equivalently, numbers k such that A058183(k) divides A037123(k).

4576 is the final term; 4 < A037123(k)/A058183(k) < 5 for all k > 4576.

Examples

			9 is a term because the average digit in 123456789 is (1+2+3+4+5+6+7+8+9)/9 = 45/9 = 5 (an integer).
122 is a term because 12345789101112..119120121122 has digit sum 1032 and digit count 258, and 1032/258 = 4 (an integer).
		

Crossrefs

Cf. A033713, A034967, A037123, A058183, A114136.

Programs

Mathematica

Flatten@ Position[ Divide @@@ Transpose[ Accumulate /@ {Total /@ #, Length /@ #} &@ IntegerDigits@ Range@ 5000], Integer] (* _Giovanni Resta, Aug 12 2018 *)