A105391 -id:A105391 - cp's OEIS frontend

A105390 Number of Hannah Rollman's numbers <= n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 9, 10, 10, 10, 11, 11, 11, 11, 11, 12, 13, 14, 15, 15, 15, 16, 16, 16, 16, 17, 18, 19, 20, 21, 21, 21, 22, 22, 22, 23, 24, 25, 26, 27, 28, 28

Offset: 1

Reinhard Zumkeller, Apr 04 2005

a(n) = #{k: A048992(k)<=n} = n - #{k: A048991(k)<=n};
a(n) < n/2 for n < 740; a(n) > n/2 for 740 < n < 1260,
see A105391 for numbers m with a(m) = m/2.

Klaus Brockhaus, Table of n, a(n) for n = 1..6000
Klaus Brockhaus, Plots of A105390(n)/n at various scales

Cf. A048991, A048992, A105391, A131981.

A131982 Numbers n such that A131981(n) = n/2.

Original entry on oeis.org

576, 584, 588, 592, 600, 1650, 1654, 3430, 3440, 3448, 3452, 3458, 3462, 3466, 3474, 3520, 3600, 3608, 3610

Offset: 1

Klaus Brockhaus, Aug 15 2007

Numbers n such that number of terms <= n of A116700 equals number of terms <= n of A131881.
Numbers n such that numbers of numbers that occur in the concatenation of 1,2,3...,n-1 equals numbers of numbers that do not occur in the concatenation of 1,2,3...,n-1.
There are no other terms <= 600000. The plots in the link strongly suggest that the sequence is complete.

			A131981(n) < n/2 for 1 <=n < 576,
A131981(n) < n/2 for 576 < n < 584,
A131981(n) > n/2 for 584 < n < 588,
A131981(n) < n/2 for 588 < n < 592,
A131981(n) > n/2 for 592 < n < 600,
A131981(n) > n/2 for 600 < n < 1650,
A131981(n) > n/2 for 1650 < n < 1654,
A131981(n) < n/2 for 1654 < n < 3430,
A131981(n) > n/2 for 3430 < n < 3440,
..............
A131981(n) < n/2 for 3608 < n <= 3610,
A131981(n) > n/2 for 3610 < n <= 600000.

Klaus Brockhaus, Plots of A131981(n)/n at various scales

Cf. A116700 (early bird numbers), A131881 (complement of A116700), A131981 (number of early bird numbers <= n), A105390 (number of Rollman numbers <= n), A105391 (numbers n such that A105390(n) = n/2).

s$ = "" : c = 0 : d = 0
FOR n = 1 TO 4000
sn$ = str$(n)
IF instr(s$, sn$) > 0 THEN d = d+1 ELSE c = c+1
s$ = s$ + sn$ : IF c = d THEN print n ; ",";
NEXT

Edited by Charles R Greathouse IV, Oct 28 2009

cp's OEIS Frontend

A105390 Number of Hannah Rollman's numbers <= n.

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A131982 Numbers n such that A131981(n) = n/2.

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