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.

A379801 Nearest integer to n*(1+sqrt(6))/2.

Original entry on oeis.org

0, 2, 3, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 22, 24, 26, 28, 29, 31, 33, 34, 36, 38, 40, 41, 43, 45, 47, 48, 50, 52, 53, 55, 57, 59, 60, 62, 64, 66, 67, 69, 71, 72, 74, 76, 78, 79, 81, 83, 85, 86, 88, 90, 91, 93, 95, 97, 98, 100, 102, 103, 105, 107, 109, 110, 112, 114, 116, 117, 119, 121, 122, 124, 126, 128, 129, 131, 133, 135
Offset: 0

Views

Author

N. J. A. Sloane, Jan 19 2025

Keywords

Comments

The floor of n*(1+sqrt(6))/2 is A379805. [Corrected by Jinyuan Wang, Jan 20 2025]

Links

Crossrefs

Cf. A000201, A379800, A379805.

Programs

  • Mathematica
    Round[Range[0, 100]*(1 + Sqrt[6])/2] (* Paolo Xausa, Jan 21 2025 *)
  • PARI
    a(n) = round(n*(1+quadgen(24))/2); \\ Michel Marcus, Jan 20 2025

A176051 Decimal expansion of (2+sqrt(6))/2.

Original entry on oeis.org

2, 2, 2, 4, 7, 4, 4, 8, 7, 1, 3, 9, 1, 5, 8, 9, 0, 4, 9, 0, 9, 8, 6, 4, 2, 0, 3, 7, 3, 5, 2, 9, 4, 5, 6, 9, 5, 9, 8, 2, 9, 7, 3, 7, 4, 0, 3, 2, 8, 3, 3, 5, 0, 6, 4, 2, 1, 6, 3, 4, 6, 2, 8, 3, 6, 2, 5, 4, 8, 0, 1, 8, 8, 7, 2, 8, 6, 5, 7, 5, 1, 3, 2, 6, 9, 9, 2, 9, 7, 1, 6, 5, 5, 2, 3, 2, 0, 1, 1, 7, 4, 0, 9, 2, 9
Offset: 1

Views

Author

Klaus Brockhaus, Apr 07 2010

Keywords

Comments

Continued fraction expansion of (2+sqrt(6))/2 is A010694.
a(n) = A115754(n) for n > 1; a(1) = 2.

Examples

			(2+sqrt(6))/2 = 2.22474487139158904909...
Note also that (1+sqrt(6))/2 = 1.724744871391589049098642..., the mis-typed golden ratio. - _N. J. A. Sloane_, Jan 19 2025

Crossrefs

Cf. A010464 (decimal expansion of sqrt(6)), A115754 (decimal expansion of sqrt(3/2)), A010694 (repeat 2, 4).
See also A379800.

Programs

  • Mathematica
    RealDigits[(2+Sqrt[6])/2,10,120][[1]]  (* Harvey P. Dale, Apr 21 2011 *)

A379805 Floor of n*(1+sqrt(6))/2.

Original entry on oeis.org

0, 1, 3, 5, 6, 8, 10, 12, 13, 15, 17, 18, 20, 22, 24, 25, 27, 29, 31, 32, 34, 36, 37, 39, 41, 43, 44, 46, 48, 50, 51, 53, 55, 56, 58, 60, 62, 63, 65, 67, 68, 70, 72, 74, 75, 77, 79, 81, 82, 84, 86, 87, 89, 91, 93, 94, 96, 98, 100, 101, 103, 105, 106, 108, 110, 112, 113, 115, 117, 119, 120, 122, 124, 125, 127, 129, 131, 132, 134, 136, 137, 139, 141, 143, 144, 146, 148, 150, 151, 153, 155, 156, 158, 160, 162, 163
Offset: 0

Views

Author

N. J. A. Sloane, Jan 20 2025

Keywords

Links

Crossrefs

Cf. A000201, A182760, A379800, A379801.

Programs

  • Mathematica
    Floor[Range[0, 100]*(1 + Sqrt[6])/2] (* Paolo Xausa, Jan 21 2025 *)

Extensions

More than the usual number of terms are shown in order to distinguish this from a very similar sequence.
Showing 1-3 of 3 results.

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

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