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

1,2

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.

Links

Table of n, a(n) for n=1..11.

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A364836 A068061 A332970 * A062887 A062886 A319585

Adjacent sequences: A316489 A316490 A316491 * A316493 A316494 A316495

Keyword

nonn,base,fini,full

Author

Jon E. Schoenfield, Aug 11 2018

Status

approved