A131981 -id:A131981 - cp's OEIS frontend

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

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

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

Original entry on oeis.org

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.

A105391 Numbers m such that there are an equal number of numbers <= m that are contained and that are not contained in the concatenation of terms <= m in A048991.

Original entry on oeis.org

740, 1260, 1262, 5230, 15804, 15814, 15816, 36294, 194876, 213868

Offset: 1

Reinhard Zumkeller, Apr 04 2005

A105390(a(n)) = a(n)/2.

There are no other terms <= 600000. The plots in a105390.gif strongly suggest that the sequence is complete. - Klaus Brockhaus, Aug 15 2007

			A105390(n) < n/2 for n < a(1)=740;
A105390(n) > n/2 for n with 740 < n < a(2)=1260;
A105390(1261)=631, A105390(a(3))=A105390(1262)=631;
A105390(n) < n/2 for n with 1262 < n < a(4)=5230;
A105390(n) > n/2 for n with 5230 < n < a(5)=15804;
A105390(n) < n/2 for n with 15804 < n < a(6)=15814;
A105390(15815)=7908, A105390(a(7))=A105390(15816)=7909;
A105390(n) < n/2 for n with 15816 < n < a(8)=36294;
A105390(n) > n/2 for n with 36294 < n < a(9)=194876; etc.

Nick Hobson, Python program for this sequence

Cf. A048991, A048992, A105390, A131982 (numbers n such that A131981(n) = n/2).

s$ = "" : c = 0 : d = 0
FOR n = 1 TO 40000
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 ' Klaus Brockhaus, Aug 15 2007

cp's OEIS Frontend

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

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JBASIC

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

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A105391 Numbers m such that there are an equal number of numbers <= m that are contained and that are not contained in the concatenation of terms <= m in A048991.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

JBASIC