A131982 -id:A131982 - cp's OEIS frontend

A131981 Number of early bird numbers <= n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 9, 9, 10, 10, 10, 10, 10, 10, 11, 12, 13, 14, 14, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20, 20, 21, 21, 21, 21, 22, 23, 24, 25, 26, 27, 27, 28, 28, 28, 29, 30, 31, 32

Offset: 1

Klaus Brockhaus, Aug 15 2007

a(n) = number of k such that A116700(k) <= n; a(n) = n - number of k such that A131881(k) <= n.

A131982 gives numbers n such that a(n) = n/2, or numbers n such that (number of k such that A116700(k) <= n) = (number of k such that A131881(k) <= n).

			There are two early bird numbers <= 21, viz. 12 and 21, hence a(21) = 2.

Klaus Brockhaus, Table of n, a(n) for n = 1..6000
Klaus Brockhaus, Plots of A131981(n)/n at various scales

Cf. A116700 (early bird numbers), A131881 (complement of A116700), A132133 (number of n-digit terms of 131881), A105390 (number of Rollman numbers <= n), A131982 (numbers n such that A131981(n) = n/2).

s$ = "" : d = 0
FOR n = 1 TO 84
sn$ = str$(n)
IF instr(s$, sn$) > 0 THEN d = d+1
s$ = s$ + sn$ : print d ; ",";
NEXT

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

A131981 Number of early bird numbers <= n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

JBASIC