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.

A336371 Numbers k such that gcd(k, prime(k) + prime(k-1)) > 1.

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100
Offset: 1

Views

Author

Clark Kimberling, Oct 04 2020

Keywords

Crossrefs

Cf. A000040, A001043, A336366, A336370, A336372, A336373.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &]  (* A336370 *)
v = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] > 1 &]   (* A336371 *)
Prime[u]  (* A336372 *)
Prime[v]  (* A336373 *)

Formula

In the following table, p(k) = A000040(k) = prime(k).
k p(k) p(k)+p(k-1) gcd
2 3 5 1
3 5 8 1
4 7 12 4
5 11 18 1
6 13 24 6
2 and 3 are in A336370; 4 and 6 are in this sequence; 3 and 5 are in A336372; 7 and 13 are in A336373.

Extensions

Offset corrected by Mohammed Yaseen, Jun 02 2023

A336373 Primes prime(k) such that gcd(k, prime(k)+prime(k-1)) > 1.

Original entry on oeis.org

7, 13, 19, 23, 29, 37, 41, 43, 47, 53, 61, 71, 73, 79, 89, 101, 103, 107, 113, 131, 139, 151, 163, 167, 173, 181, 193, 197, 199, 223, 229, 233, 239, 251, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 383, 397, 409, 419, 421, 433, 443
Offset: 1

Views

Author

Clark Kimberling, Oct 05 2020

Keywords

Comments

This sequence and A336372 partition the set of odd primes.

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n)+p(n-1)   gcd
  2     3         5          1
  3     5         8          1
  4     7        12          4
  5    11        18          1
  6    13        24          6
2 and 3 are in A336370; 4 and 6 are in A336371; 3 and 5 are in A336372; 7 and 13 are in this sequence.

Crossrefs

Cf. A000040, A336366, A336370, A336371, A336372.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &]  (* A336370 *)
v = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] > 1 &]   (* A336371 *)
Prime[u]  (* A336372 *)
Prime[v]  (* A336373 *)

Extensions

Offset corrected by Mohammed Yaseen, Jul 16 2023

A336372 Primes prime(k) such that gcd(k, prime(k) + prime(k-1)) = 1.

Original entry on oeis.org

3, 5, 11, 17, 31, 59, 67, 83, 97, 109, 127, 137, 149, 157, 179, 191, 211, 227, 241, 257, 277, 283, 331, 353, 367, 379, 389, 401, 431, 439, 449, 461, 467, 509, 547, 563, 587, 599, 607, 617, 653, 691, 709, 739, 751, 773, 797, 823, 829, 859, 877, 907, 919, 947
Offset: 1

Views

Author

Clark Kimberling, Oct 05 2020

Keywords

Comments

This sequence and A336373 partition the set of odd primes.

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n)+p(n-1)   gcd
  2     3         5          1
  3     5         8          1
  4     7        12          4
  5    11        18          1
  6    13        24          6

Crossrefs

Cf. A000040, A001043, A336366, A336370, A336371, A336373.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &]  (* A336370 *)
v = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] > 1 &]   (* A336371 *)
Prime[u]  (* this sequence *)
Prime[v]  (* A336373 *)

Extensions

Offset corrected by Mohammed Yaseen, Jun 02 2023
Showing 1-3 of 3 results.

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

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