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.

Previous Showing 51-56 of 56 results.

A075975 Positions of check bits in code in A075973.

Original entry on oeis.org

262143, 133956095, 2021408271, 6872157809, 11453421238, 20188081042, 31219700917, 37548876508, 74341529658, 145177797287, 249195030418, 326072676800, 638246908359, 992606833010, 1443854701806
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

References

  • J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Transactions on Information Theory, 32:337-348, 1986.

Links

Crossrefs

Cf. A075928, A075929, A075930, A075973, A075974, A075978, A075969.

A075927 Basis for code in A075926.

Original entry on oeis.org

7, 25, 42, 75, 385, 642, 1155, 2184, 4233, 8330, 16523, 98305, 163842, 294915, 557064, 1081353, 2129930, 4227083, 8421504, 16810113, 33587330, 67141763, 134250632, 268468361, 536903818, 1073774731, 6442450945, 10737418242
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

Links

Crossrefs

Cf. A075928, A075929, A075930, A075926, A057716, A075933.

Formula

a(n) = b(2^n), where b is the Hamming code d=3.
b(n) = XOR(a(i)) where i is a bit set in n.

A235336 Numbers having evil number of 1's in their binary representation.

Original entry on oeis.org

0, 7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 31, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 63, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 95, 97, 98, 100, 103, 104, 107, 109, 110, 111, 112, 115, 117, 118, 119, 121, 122, 123, 124, 125, 126, 131
Offset: 0

Views

Author

Vladimir Shevelev, Jan 06 2014

Keywords

Comments

A000120(a(n)) is in A001969.
Except for 0, the first term in which the sequence differs from A075930 is the 27th: a(27) = 63.
Also a(27) = 63 is the first odd term that is not in A092246. - Altug Alkan, Mar 18 2018

Examples

			7 in binary has 3 1's and since 3 is evil (i.e., belongs to A001969), then 7 is in the sequence.

Links

Crossrefs

Cf. A000120, A001969, A075930, A092246.

Programs

  • Maple
    filter:= n ->
  convert(convert(convert(convert(n,base,2),`+`),base,2),`+`)::even:
select(filter, [$0..131]); # Robert Israel, Mar 18 2018
  • Mathematica
    Select[Range[0, 150], EvenQ[DigitCount[DigitCount[#, 2, 1], 2, 1]] &] (* Amiram Eldar, Jul 24 2023 *)

A271499 Positive numbers n such that the number of 1's in the binary expansion of n is not a power of 2.

Original entry on oeis.org

7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 31, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 63, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 95, 97, 98, 100, 103, 104, 107, 109, 110, 111, 112, 115, 117, 118, 119, 121, 122, 123, 124, 125, 126, 127, 131, 133, 134, 137, 138, 140
Offset: 1

Views

Author

N. J. A. Sloane, Apr 16 2016

Keywords

Examples

			127 = 1111111_2 has seven 1's, so is a term (this distinguishes the sequence from A235336).

Links

Crossrefs

Complement of A143071.
Similar to but different from A075930, A235336 and A271500.

Programs

  • Mathematica
    Select[Range@ 140, ! IntegerQ@ Log2@ First@ DigitCount[#, 2] &] (* Michael De Vlieger, Apr 16 2016 *)
  • PARI
    lista(nn) = {for (n=1, nn, my(nbd = hammingweight(n)); if (!((nbd==1) || (nbd==2) || (ispower(nbd,,&k) && (k==2))), print1(n, ", ")););} \\ Michel Marcus, Apr 16 2016
  • Python
    A271499_list = [n for n in range(1,10**6) if bin(bin(n).count('1')).count('1') != 1] # Chai Wah Wu, Apr 16 2016

A178307 Remove powers of 2 from A000069. Let b(n) be n-th term of the remaining sequence. Then a(n) is the least number m such that (b(n))^m is in A001969.

Original entry on oeis.org

3, 3, 2, 3, 3, 2, 3, 4, 2, 3, 3, 4, 2, 3, 3, 2, 3, 2, 4, 4, 2, 3, 3, 5, 2, 3, 4, 2, 4, 2, 2, 3, 4, 2, 3, 2, 3, 3, 3, 2, 2, 4, 4, 4, 9, 2, 2, 2, 3, 3, 2, 4, 5, 3, 2, 3, 3, 4, 2, 4, 2, 2, 4, 3, 3, 2, 2, 2, 3, 2, 4, 4, 2, 2, 3, 4, 2, 2, 4, 3, 3, 4, 5, 3, 5, 2, 2, 2, 6, 4, 4, 2, 4, 2, 2, 9, 2, 2, 2, 2, 3, 2, 3, 3, 3
Offset: 1

Views

Author

Vladimir Shevelev, May 24 2010, May 25 2010

Keywords

Comments

The sequence {b(n)} coincides with A075930. Conjecture. For every n>=1, a(n) does exist.
The sequence b(n) is A075930 (Positions of check bits in code in A075928); see comment in that sequence. [From Jeremy Gardiner, May 26 2010]

Crossrefs

Cf. A000069 A001969 A178253
Cf. A075930. [From Jeremy Gardiner, May 26 2010]

Formula

If k=b(n)=2^m*b(s), where b(s) is odd, then a(n)=a(s).

Extensions

Edited by N. J. A. Sloane, May 29 2010
Extended by Jeremy Gardiner, May 26 2010

A377464 Number of connected pairs of subsets of [n] with each being a different size.

Original entry on oeis.org

0, 0, 2, 12, 62, 290, 1292, 5579, 23606, 98490, 406862, 1668689, 6807704, 27663441, 112076057, 453031502, 1828018406, 7366128866, 29650536878, 119249689265, 479277846962, 1925216817095, 7729973578307, 31025341749680, 124486445913728, 499362094315865
Offset: 0

Views

Author

John Tyler Rascoe, Oct 29 2024

Keywords

Comments

Empirically, a(A075930(n)) == 1 (mod 2).

Examples

			a(3) = 12 counts the pairs: {{1,2},{1}}, {{1,2},{2}}, {{1,3},{1}}, {{1,3},{3}}, {{2,3},{2}}, {{2,3},{3}}, {{1,2,3},{1,2}}, {{1,2,3},{1,3}}, {{1,2,3},{2,3}}, {{1,2,3},{1}}, {{1,2,3},{2}}, {{1,2,3},{3}}.

Crossrefs

Cf. A001187, A075930, A323818, A326749.

Programs

  • PARI
    A377464(n) = {sum(i=0,n-2,binomial(n,i)*sum(j=i+1,n-1, binomial(n,j)-binomial(i,n-j)))}

Formula

a(n) = Sum_{i=0..n-2} binomial(n,i) * Sum_{j=i+1..n-1} (binomial(n,j) - binomial(i,n-j)).
Previous Showing 51-56 of 56 results.

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