cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A228091 Numbers n for which there exists such a natural number k < n that k + bitcount(k) = n + bitcount(n), where bitcount(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

Original entry on oeis.org

4, 12, 16, 17, 20, 28, 32, 34, 36, 44, 48, 49, 52, 60, 65, 68, 76, 80, 81, 84, 92, 96, 98, 100, 108, 112, 113, 116, 124, 128, 129, 130, 131, 132, 140, 144, 145, 148, 156, 160, 162, 164, 172, 176, 177, 180, 188, 193, 196, 204, 208, 209, 212, 220, 224, 226, 228
Offset: 1

Views

Author

Antti Karttunen, Aug 09 2013

Keywords

Comments

In other words, all such terms A228236(n) which satisfy A228236(n) > A228086(A092391(A228236(n))), which means that the sequence contains all natural numbers n such that A228085(A092391(n)) > 1 and n > A228086(A092391(n)).
Note: 124 is the first term that occurs both here and in A228237.

Examples

			For cases 0 + A000120(0) = 0, 1 + A000120(1) = 2, 2 + A000120(2) = 3, 3 + A000120(3) = 5 there are no smaller solutions yielding the same result.
However, for 4 + A000120(4) = 5, we already saw the case 3+A000120(3) giving the same result, thus 4 is the first term of this sequence.
Next time this occurs for 12, as 12 + A000120(12) = 14 = 11 + A000120(11), and 11 < 12.

Links

Crossrefs

Subset of A228236. Cf. also A228237. Complement of this sequence gives the nonzero terms of A228086 in ascending order.
Cf. A228085, A228086, A092391.

A228090 Numbers k for which a sum k + bitcount(k) cannot be obtained as a sum k2 + bitcount(k2) for any other k2<>k . Here bitcount(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

Original entry on oeis.org

0, 1, 2, 5, 6, 7, 8, 9, 10, 13, 18, 21, 22, 23, 24, 25, 26, 30, 33, 37, 38, 39, 40, 41, 42, 45, 50, 53, 54, 55, 56, 57, 58, 61, 63, 64, 66, 69, 70, 71, 72, 73, 74, 77, 82, 85, 86, 87, 88, 89, 90, 94, 97, 101, 102, 103, 104, 105, 106, 109, 114, 117, 118, 119, 120
Offset: 1

Views

Author

Antti Karttunen, Aug 17 2013

Keywords

Comments

In other words, numbers k such that A228085(A092391(k)) = 1.

Examples

			0 is in this sequence because the sum 0+A000120(0)=0 cannot be obtained with any other value of k than k=0.
1 is in this sequence because the sum 1+A000120(1)=2 cannot be obtained with any other value of k than k=1.
2 is in this sequence because the sum 2+A000120(2)=3 cannot be obtained with any other value of k than k=2.
3 is not in this sequence because the sum 3+A000120(3)=5 can also be obtained with value k=4, as also 4+A000120(4)=5.

Links

Crossrefs

Sequence A228089 sorted into ascending order. Complement: A228236.
Cf. also A092391, A228085, A228088.

A228237 Numbers n for which there exists such a natural number k > n that k + bitcount(k) = n + bitcount(n), where bitcount(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

Original entry on oeis.org

3, 11, 14, 15, 19, 27, 29, 31, 35, 43, 46, 47, 51, 59, 62, 67, 75, 78, 79, 83, 91, 93, 95, 99, 107, 110, 111, 115, 123, 124, 125, 126, 127, 131, 139, 142, 143, 147, 155, 157, 159, 163, 171, 174, 175, 179, 187, 190, 195, 203, 206, 207, 211, 219, 221, 223, 227
Offset: 1

Views

Author

Antti Karttunen, Sep 11 2013

Keywords

Comments

In other words, all such terms A228236(n) which satisfy A228236(n) < A228087(A092391(A228236(n))).
Note: 124 is the first term that occurs both here and in A228091.

Examples

			For cases 0 + A000120(0) = 0, 1 + A000120(1) = 2, 2 + A000120(2) = 3 there are no larger solutions yielding the same result.
However, for 3 + A000120(3) = 5 there is a larger solution yielding the same result, namely 4 + A000120(4) = 5, thus 3 is the first term of this sequence.
Next time this occurs for 11, as 11 + A000120(11) = 14 = 12 + A000120(12), and 12 > 11.

Links

Crossrefs

Subset of A228236. Cf. also A228091.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.