A272756 -id:A272756 - cp's OEIS frontend

A065880 Largest positive number that is n times the number of 1's in its binary expansion, or 0 if no such number exists.

0, 1, 2, 6, 4, 10, 12, 21, 8, 18, 20, 55, 24, 0, 42, 60, 16, 34, 36, 0, 40, 126, 110, 115, 48, 0, 0, 108, 84, 116, 120, 155, 32, 66, 68, 0, 72, 222, 0, 156, 80, 246, 252, 172, 220, 180, 230, 0, 96, 0, 0, 204, 0, 318, 216, 0, 168, 285, 232, 295, 240, 366, 310, 378, 64, 130

Offset: 0

Henry Bottomley, Nov 26 2001

a(n) is bounded above by n*A272756(n), so a program only has to check values up to that point to see if a(n) is zero. - Peter Kagey, May 05 2016

			a(23)=115 since 115 is written in binary as 1110011 and 115/(1+1+1+0+0+1+1)=23 and there is no higher possibility (if k is more than 127 then k divided by its number of binary 1's is more than 26).

Peter Kagey, Table of n, a(n) for n = 0..10000

A052489 is the base 10 equivalent.

Cf. A000120, A049445, A058898, A065413, A065878, A065879, A272756.

Table[SelectFirst[Reverse@ Range@ #, First@ DigitCount[#, 2] == #/n &] &[n SelectFirst[Range[2^12], # > IntegerLength[n #, 2] &]], {n, 80}] /. k_ /; MissingQ@ k -> 0 (* Michael De Vlieger, May 05 2016, Version 10.2 *)

A065879 a(n) is the smallest positive number that is n times the number of 1's in its binary expansion, or 0 if no such number exists.

Original entry on oeis.org

1, 2, 6, 4, 10, 12, 21, 8, 18, 20, 55, 24, 0, 42, 60, 16, 34, 36, 0, 40, 126, 110, 69, 48, 0, 0, 81, 84, 116, 120, 155, 32, 66, 68, 0, 72, 185, 0, 156, 80, 205, 252, 172, 220, 180, 138, 0, 96, 0, 0, 204, 0, 212, 162, 0, 168, 228, 232, 295, 240, 366, 310, 378, 64, 130

Offset: 1

Henry Bottomley, Nov 26 2001

a(n) is bounded above by n*A272756(n), so a program only has to check values up to that point to see if a(n) is zero. - Peter Kagey, May 05 2016

			a(23) is 69 since 69 is written in binary as 1000101, 69/(1+0+0+0+1+0+1)=23 and there is no smaller possibility (neither 23 nor 46 are divisible by their number of binary 1's).

Peter Kagey, Table of n, a(n) for n = 1..10000

A003634 is the base-10 equivalent.

Cf. A000120, A049445, A058898, A065413, A065878, A065880, A272756.

Table[SelectFirst[Range[2^12], # == n First@ DigitCount[#, 2] &] /. k_ /; MissingQ@ k -> 0, {n, 80}] (* Michael De Vlieger, May 05 2016, Version 10.2 *)

A272759 a(n) = A065879(n)/n.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 5, 2, 0, 3, 4, 1, 2, 2, 0, 2, 6, 5, 3, 2, 0, 0, 3, 3, 4, 4, 5, 1, 2, 2, 0, 2, 5, 0, 4, 2, 5, 6, 4, 5, 4, 3, 0, 2, 0, 0, 4, 0, 4, 3, 0, 3, 4, 4, 5, 4, 6, 5, 6, 1, 2, 2, 0, 2, 5, 0, 4, 2, 6, 5, 4, 0, 4, 4, 5, 2, 5, 5, 4, 6, 4, 4, 3

Offset: 1

Peter Kagey, May 05 2016

This sequence is bounded above by A272756.

a(n) is the least value i such that A000120(n * i) = i or 0 if no such value exists.

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A000120, A065879, A272756, A272760.

Table[(SelectFirst[Range[2^12], # == n First@ DigitCount[#, 2] &] /.
    k_ /; MissingQ@ k -> 0)/n, {n, 120}] (*  *)

A272760 a(n) = A065880(n)/n.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 5, 2, 0, 3, 4, 1, 2, 2, 0, 2, 6, 5, 5, 2, 0, 0, 4, 3, 4, 4, 5, 1, 2, 2, 0, 2, 6, 0, 4, 2, 6, 6, 4, 5, 4, 5, 0, 2, 0, 0, 4, 0, 6, 4, 0, 3, 5, 4, 5, 4, 6, 5, 6, 1, 2, 2, 0, 2, 6, 0, 5, 2, 6, 6, 4, 0, 6, 4, 6, 2, 6, 6, 6, 6, 5, 4, 3

Offset: 1

Peter Kagey, May 05 2016

This sequence is bounded above by A272756.

a(n) is the greatest value i such that A000120(n * i) = i or 0 if no such value exists.

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A065880, A272756, A272759.

Table[SelectFirst[Reverse@ Range@ #, First@ DigitCount[#, 2] == #/n &] &[n SelectFirst[Range[2^12], # > IntegerLength[n #, 2] &]]/n, {n, 120}] /. k_ /; MissingQ@ k -> 0 (* Michael De Vlieger, May 05 2016, Version 10.2 *)

cp's OEIS Frontend

A065880 Largest positive number that is n times the number of 1's in its binary expansion, or 0 if no such number exists.

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A065879 a(n) is the smallest positive number that is n times the number of 1's in its binary expansion, or 0 if no such number exists.

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A272759 a(n) = A065879(n)/n.

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A272760 a(n) = A065880(n)/n.

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