A136413 a(1)=1. a(n+1) = a(n) + (number of terms of this sequence that are <= (1/n)sum{k=1 to n} a(k)).

1, 2, 3, 5, 7, 10, 13, 17, 22, 27, 33, 39, 46, 54, 62, 71, 80, 90, 100, 111, 123, 135, 148, 161, 175, 189, 204, 220, 236, 253, 270, 288, 306, 325, 345, 365, 386, 407, 429, 451, 474, 498, 522, 547, 572, 598, 625, 652, 680, 708, 737, 766, 796, 827, 858, 890, 922

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

The sum of the first 7 terms of this sequence is 1+2+3+5+7+10+13 = 41. So the arithmetic average of the first 7 terms is 41/7. The terms of this sequence that are <= 41/7 (= 5 +6/7) are 1,2,3,5. There are therefore 4 such terms <= 41/7. So a(8) = a(7) + 4 = 13 + 4 = 17.

Mathematica

cnt = Function[a, Length@Select[a, # <= Total[a]/Length[a] &]]; Nest[Append[#, #[[-1]] + cnt[#]] &, {1}, 56] (* Ivan Neretin, May 21 2018*)

Crossrefs

Sequence in context: A025700 A033638 A194205 * A177337 A117143 A253170

Adjacent sequences: A136410 A136411 A136412 * A136414 A136415 A136416

Keyword

nonn

Author

Leroy Quet, Mar 31 2008

Extensions

More terms from Sean A. Irvine, May 03 2010

Status

approved