A228089 -id:A228089 - cp's OEIS frontend

A228088 Numbers n for which there is a unique k which satisfies n = k + wt(k), where wt(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

0, 2, 3, 7, 8, 9, 10, 11, 12, 16, 20, 24, 25, 26, 27, 28, 29, 34, 35, 40, 41, 42, 43, 44, 45, 49, 53, 57, 58, 59, 60, 61, 62, 65, 66, 68, 69, 72, 73, 74, 75, 76, 77, 81, 85, 89, 90, 91, 92, 93, 94, 99, 100, 105, 106, 107, 108, 109, 110, 114, 118, 122, 123, 124

Offset: 1

Antti Karttunen, Aug 09 2013

wt(k) = A000120(k) is also called bitcount(k).
In other words, the positions of ones in A228085.
Numbers that can be expressed as the sum of distinct terms of the form 2^n+1, n=0,1,... in exactly one way. - Matthew C. Russell, Oct 08 2013

			0 is in this sequence because there is a unique k such that k+A000120(k)=0, in this case k=0.
1 is not in this sequence because there is no such k that k+A000120(k) would be 1. (Instead 1 is in A010061).
2 is in this sequence because there is exactly one k that satisfies k+A000120(k)=2, namely k=1.
3 is in this sequence because there is exactly one k that satisfies k+A000120(k)=3, namely k=2.
4 is not in this sequence because there is no such k that k+A000120(k) would be 4. (Instead 4 is in A010061.)
5 is not in this sequence because there is more than one k that satisfies k+A000120(k)=5, namely k=3 and k=4.

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

Subset of A228082.
Cf. A228089 (corresponding k's for each a(n)).
Cf. A228090 (the same k's sorted into ascending order).
Cf. A000120, A228085, A092391, A010061, A010062, A230091, A230092, A230058.
Cf. A227915.

a228088 n = a228088_list !! (n-1)
a228088_list = 0 : filter ((== 1) . a228085) [1..]
-- Reinhard Zumkeller, Oct 13 2013

For Maple code see A230091. - N. J. A. Sloane, Oct 10 2013

a(n) = A092391(A228089(n)). [Consequence of the definitions of A228088 & A228089. Use the given Scheme-code to actually compute the sequence]

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

Antti Karttunen, Aug 17 2013

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

			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.

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

Sequence A228089 sorted into ascending order. Complement: A228236.

Cf. also A092391, A228085, A228088.

cp's OEIS Frontend

A228088 Numbers n for which there is a unique k which satisfies n = k + wt(k), where wt(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

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