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 1-4 of 4 results.

A383193 The lexicographically earliest "mean-central" sequence, as is defined in A383192.

Original entry on oeis.org

1, 3, 5, 6, 10, 11, 12, 13, 19, 20, 21, 23, 25, 26, 27, 28, 36, 37, 38, 39, 41, 42, 46, 47, 49, 51, 53, 55, 56, 57, 58, 59, 69, 70, 71, 72, 73, 75, 77, 78, 82, 83, 84, 85, 91, 92, 93, 94, 98, 99, 101, 102, 106, 107, 109, 111, 113, 115, 117, 118, 119, 120
Offset: 1

Views

Author

Yifan Xie, Apr 20 2025

Keywords

Links

Crossrefs

Cf. A383192, A383194.

A383194 The least number of times that b(k) = 2*k - 1 for the first n terms of a "mean-central" sequence, as is defined in A383192.

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 10, 10, 10, 10, 10, 11, 11
Offset: 1

Views

Author

Yifan Xie, Apr 21 2025

Keywords

Comments

Problem 2 of the 2025 European Girls' Mathematical Olympiad implies that a(n) -> oo as n -> oo.

Links

Crossrefs

Cf. A383192, A383193.

A384191 Unique increasing sequence (a(n)) whose complement, (b(n)), satisfies b(n) = a(a(n))+3.

Original entry on oeis.org

1, 2, 3, 7, 8, 9, 10, 11, 12, 16, 17, 18, 22, 23, 24, 25, 26, 27, 31, 32, 33, 34, 35, 36, 40, 41, 42, 46, 47, 48, 49, 50, 51, 55, 56, 57, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 79, 80, 81, 85, 86, 87, 88, 89, 90, 94, 95, 96, 97, 98, 99, 103, 104
Offset: 1

Views

Author

Clark Kimberling, May 21 2025

Keywords

Comments

For k>=1, the Mathematica program gives solutions of the complementary equation b(n)=a(a(n))+k; if k=1, then a=A000201; if k=2, then a=A137708.

Examples

			a(a(1)) = a(1) = 1, so b(1) = 4.
a(a(2)) = a(2) = 2, so b(2) = 5.
a(a(3)) = a(3) = 3, so b(3) = 6.
a(a(4)) = a(7) = 10, so b(4) = 13.

Crossrefs

Cf. A000201, A137708, A384192 (complement).

Programs

  • Mathematica
    k = 3; p = k*Array[Floor[#*GoldenRatio] &, 100] ;
seq = ConstantArray[1, Last[p]];
seq[[p]] = k + 1;
u = Join[{1}, Accumulate[seq] + 1]  (* A384191 *)
Complement[Range[Last[#]], #] &[u]  (* A383192 *)
(* Peter J. C. Moses, May 12 2025 *)

A384192 Complement of A384191.

Original entry on oeis.org

4, 5, 6, 13, 14, 15, 19, 20, 21, 28, 29, 30, 37, 38, 39, 43, 44, 45, 52, 53, 54, 58, 59, 60, 67, 68, 69, 76, 77, 78, 82, 83, 84, 91, 92, 93, 100, 101, 102, 106, 107, 108, 115, 116, 117, 121, 122, 123, 130, 131, 132, 139, 140, 141, 145, 146, 147, 154, 155
Offset: 1

Views

Author

Clark Kimberling, May 21 2025

Keywords

Crossrefs

Cf. A137709, A384191 (complement).

Programs

  • Mathematica
    k = 3; p = k*Array[Floor[#*GoldenRatio] &, 100] ;
seq = ConstantArray[1, Last[p]];
seq[[p]] = k + 1;
u = Join[{1}, Accumulate[seq] + 1]  (* A384191 *)
Complement[Range[Last[#]], #] &[u]  (* A383192 *)
(* Peter J. C. Moses, May 12 2025 *)
Showing 1-4 of 4 results.

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

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