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.

A358528 a(n) = n-th prime p(k) such that p(k) - p(k-1) > p(k-1) - p(k-2).

Original entry on oeis.org

5, 11, 17, 23, 29, 37, 47, 53, 67, 79, 89, 97, 107, 113, 127, 137, 149, 157, 173, 191, 197, 211, 233, 239, 251, 277, 293, 307, 317, 331, 347, 353, 359, 367, 389, 397, 409, 419, 431, 439, 449, 457, 467, 479, 499, 509, 521, 541, 557, 577, 587, 607, 631, 647
Offset: 1

Views

Author

Clark Kimberling, Nov 21 2022

Keywords

Comments

This sequence, together with A358530 and A181424, partition the set of primes >= 5. The corresponding sequences of indices, A358529, A358531, and A356347, partition the set of positive integers >= 3.

Examples

			   n      1   2   3   4   5   6   7
   k      3   5   7   9  10  12  15
   p(n)   5  11  17  23  29  37  47

Crossrefs

Cf. A358529, A358530, A358531, A181424, A356347.

Programs

  • Mathematica
    t = Select[2 + Range[140],
Prime[#] - Prime[# - 1] > Prime[# - 1] - Prime[# - 2] &]  (* A358529 *)
Prime[t]  (* A358528 *)

A358529 Indices of the primes in A358528.

Original entry on oeis.org

3, 5, 7, 9, 10, 12, 15, 16, 19, 22, 24, 25, 28, 30, 31, 33, 35, 37, 40, 43, 45, 47, 51, 52, 54, 59, 62, 63, 66, 67, 69, 71, 72, 73, 77, 78, 80, 81, 83, 85, 87, 88, 91, 92, 95, 97, 98, 100, 102, 106, 107, 111, 115, 118, 119, 122, 124, 125, 126, 128, 133, 136
Offset: 1

Views

Author

Clark Kimberling, Nov 21 2022

Keywords

Comments

This sequence, together with A358531 and A356347, partition the set of positive integers >= 3.

Examples

			  n      1   2   3   4   5   6   7
  k      3   5   7   9  10  12  15
  p(n)   5  11  17  23  29  37  47

Crossrefs

Cf. A358528, A358530, A358531, A181424, A356347.

Programs

  • Mathematica
    t = Select[2 + Range[140],
Prime[#] - Prime[# - 1] > Prime[# - 1] - Prime[# - 2] &]  (* A358529 *)
Prime[t]  (* A358528 *)

Formula

a(n) = A233671(n) + 1.

A358530 a(n) = n-th prime prime(k) such that prime(k) - prime(k-1) < prime(k-1) - prime(k-2).

Original entry on oeis.org

13, 19, 31, 41, 43, 61, 71, 73, 83, 101, 103, 109, 131, 139, 151, 167, 181, 193, 199, 227, 229, 241, 257, 271, 281, 283, 311, 313, 337, 349, 373, 383, 401, 421, 433, 443, 461, 463, 487, 491, 503, 523, 547, 563, 571, 593, 601, 617, 619, 641, 643, 661, 677
Offset: 1

Views

Author

Clark Kimberling, Nov 21 2022

Keywords

Comments

This sequence, together with A358528 and A181424, partition the set of primes >= 5. The corresponding sequences of indices, A358531, A358529, and A356347, partition the set of positive integers >= 3.

Examples

			  n           1   2   3   4   5   6   7
  k           6   8  11  13  14  18  20
  prime(n)   13  19  31  41  43  61  71

Crossrefs

Cf. A001223, A051634, A079419, A358528, A358529, A358531, A181424, A356347.

Programs

  • Mathematica
    t = Select[2 + Range[140],
Prime[#] - Prime[# - 1] < Prime[# - 1] - Prime[# - 2] &]  (* A358531 *)
Prime[t]  (* A358530 *)

Formula

a(n) = A151800(A051634(n)). - Andrew Howroyd, Sep 21 2024

Extensions

Incorrect formula removed by Georg Fischer, Sep 21 2024

A358531 Indices of the primes in A358530.

Original entry on oeis.org

6, 8, 11, 13, 14, 18, 20, 21, 23, 26, 27, 29, 32, 34, 36, 39, 42, 44, 46, 49, 50, 53, 55, 58, 60, 61, 64, 65, 68, 70, 74, 76, 79, 82, 84, 86, 89, 90, 93, 94, 96, 99, 101, 103, 105, 108, 110, 113, 114, 116, 117, 121, 123, 127, 129, 130, 132, 134, 135, 137
Offset: 1

Views

Author

Clark Kimberling, Nov 21 2022

Keywords

Comments

This sequence, together with A358529 and A356347, partition the set of positive integers >= 3.

Examples

			  n       1   2   3   4   5   6   7
  k       6   8  11  13  14  18  20
  p(n)   13  19  31  41  43  61  71

Crossrefs

Cf. A001223, A258026, A358528, A358529, A358530, A181424, A356347.

Programs

  • Mathematica
    t = Select[2 + Range[140],
Prime[#] - Prime[# - 1] < Prime[# - 1] - Prime[# - 2] &]  (* A358531 *)
Prime[t]  (* A358530 *)

Formula

a(n) = A258026(n) + 2.
Showing 1-4 of 4 results.

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

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