A228237 -id:A228237 - cp's OEIS frontend

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.

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

Antti Karttunen, Aug 09 2013

nonn

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.

			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.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for Colombian or self numbers and related sequences

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

Cf. A228085, A228086, A092391.

A228236 Numbers k for which a sum k+bitcount(k) can be also obtained as a sum k2 +bitcount(k2) for some 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

3, 4, 11, 12, 14, 15, 16, 17, 19, 20, 27, 28, 29, 31, 32, 34, 35, 36, 43, 44, 46, 47, 48, 49, 51, 52, 59, 60, 62, 65, 67, 68, 75, 76, 78, 79, 80, 81, 83, 84, 91, 92, 93, 95, 96, 98, 99, 100, 107, 108, 110, 111, 112, 113, 115, 116, 123, 124, 125, 126, 127, 128

Offset: 1

Antti Karttunen, Aug 17 2013

nonn

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

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

Antti Karttunen, Table of n, a(n) for n = 1..10000

Complement: A228090. Subsets: A228091, A228237. Cf. also A092391, A228085.

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs