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.

A278107 a(n) is the first k such that A277515(k) is the n-th prime.

Original entry on oeis.org

1, 49, 5, 21, 10, 174, 27, 223, 1656, 3901, 1286, 1847, 5095, 3117, 5678, 1727, 14844, 23678, 10986, 33868, 41241, 42794, 50451, 35301, 39546, 206241, 10561, 89600, 50075, 87273, 75922, 142760, 3493, 236213, 277242, 805287, 619149, 333339
Offset: 2

Views

Author

Robert G. Wilson v, Nov 17 2016, and Jason Kimberley, Dec 11 2016

Keywords

Comments

Eggleton et al. show that every prime greater than two occurs in A277515; moreover, each such prime occurs an infinite number of times.

References

  • R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted.

Links

Crossrefs

Cf. A000040, A277515.

Formula

A277515(a(n)) = A000040(n).

A277644 Beatty sequence for sqrt(6)/2.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 78, 79, 80, 82, 83, 84, 85, 86
Offset: 1

Views

Author

Jason Kimberley, Oct 26 2016

Keywords

Comments

Eggleton et al. show that k is in this sequence if and only if A277515(k)=3.

Examples

			a(5)=6 because the quotient of 3*5^2 by 2 is 37 which lies between 6^2 and 7^2.

References

  • R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted.

Links

Crossrefs

Cf. A000196, A032528, A115754, A277515. Complement of A277645.

Programs

  • Magma
    [Isqrt(3*n^2 div 2): n in [1..60]];
  • Mathematica
    Floor[Range[100]*Sqrt[3/2]] (* Paolo Xausa, Jul 11 2024 *)
  • PARI
    a(n)=sqrtint(3*n^2\2) \\ Charles R Greathouse IV, Jul 11 2024

Formula

a(n) = floor(n*sqrt(6)/2).
a(n) = A000196(A032528(n)).

A277645 Beatty sequence for 3+sqrt(6).

Original entry on oeis.org

5, 10, 16, 21, 27, 32, 38, 43, 49, 54, 59, 65, 70, 76, 81, 87, 92, 98, 103, 108, 114, 119, 125, 130, 136, 141, 147, 152, 158, 163, 168, 174, 179, 185, 190, 196, 201, 207, 212, 217, 223, 228, 234, 239, 245, 250, 256, 261, 267, 272, 277, 283, 288, 294, 299, 305
Offset: 1

Views

Author

Jason Kimberley, Oct 26 2016

Keywords

Comments

Eggleton et al. show that k is in this sequence if and only if A277515(k) > 3.

Examples

			a(4) = 3*4 + 9 because 9^2 = 81 < 6*4^2 = 96 < 100 = 10^2.

References

  • R. B. Eggleton, J. S. Kimberley, and J. A. MacDougall, Square-free rank of integers, submitted.

Links

Crossrefs

Cf. A000196, A008585, A010464, A033581, A277515.
Complement of A277644.

Programs

  • Magma
    [3*n+Isqrt(6*n^2): n in [1..60]];
  • Mathematica
    Floor[Range[100]*(3 + Sqrt[6])] (* Paolo Xausa, Jul 11 2024 *)

Formula

a(n) = floor(n*(3+sqrt(6))).
a(n) = 3*n + A000196(A033581(n)).
a(n) = A008585(n) + A000196(A033581(n)).
Showing 1-3 of 3 results.

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

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