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.

A336375 Numbers k such that gcd(k, prime(k) + prime(k+2)) > 1.

Original entry on oeis.org

2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110
Offset: 1

Views

Author

Clark Kimberling, Oct 06 2020

Keywords

Comments

This sequence and A336374 partition the positive integers.

Examples

			In the following table, p(k) = A000040(k) = prime(k).
  k    p(k)   p(k)+p(k+2)   gcd
  1     2         7          1
  2     3        10          2
  3     5        16          1
  4     7        20          4
  5    11        28          1
  6    13        32          2
1 and 3 are in A336374; 2 and 4 are in this sequence; 2 and 5 are in A336376; 3 and 7 are in A336377.

Crossrefs

Cf. A000040, A336366, A336374, A336376, A336377.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 2]] == 1 &]  (* A336374 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 2]] > 1 &]   (* A336375 *)
Prime[u]  (* A336376 *)
Prime[v]  (* A336377 *)

A336376 Primes p(n) such that gcd(n, prime(n)+prime(n+2)) = 1.

Original entry on oeis.org

2, 5, 11, 17, 31, 41, 47, 59, 67, 83, 103, 109, 127, 149, 157, 167, 179, 191, 211, 227, 241, 257, 277, 283, 307, 313, 331, 347, 353, 367, 389, 401, 419, 431, 439, 449, 461, 467, 487, 499, 509, 523, 547, 563, 587, 599, 617, 631, 653, 661, 709, 727, 739, 761
Offset: 1

Views

Author

Clark Kimberling, Oct 06 2020

Keywords

Comments

This sequence and A336377 partition the set of primes.

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n)+p(n+2)   gcd
  1     2         7          1
  2     3        10          2
  3     5        16          1
  4     7        20          4
  5    11        28          1
  6    13        32          2
1 and 3 are in A336374; 2 and 4 are in A336375; 2 and 5 are in A336376; 3 and 7 are in A336377.

Crossrefs

Cf. A000040, A336366, A336374, A336375, A336377.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 2]] == 1 &]  (* A336374 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 2]] > 1 &]   (* A336375 *)
Prime[u]  (* A336376 *)
Prime[v]  (* A336377 *)

A336374 Numbers k such that gcd(k, prime(k) + prime(k+2)) = 1.

Original entry on oeis.org

1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 27, 29, 31, 35, 37, 39, 41, 43, 47, 49, 53, 55, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 113, 115, 119, 121, 127, 129, 131, 135, 137, 139, 141, 143, 147, 149, 151
Offset: 1

Views

Author

Clark Kimberling, Oct 06 2020

Keywords

Comments

This sequence and A336374 partition the positive integers.

Examples

			In the following table, p(k) = A000040(k) = prime(k).
  k    p(k)   p(k)+p(k+2)   gcd
  1     2         7          1
  2     3        10          2
  3     5        16          1
  4     7        20          4
  5    11        28          1
  6    13        32          2
1 and 3 are in this sequence; 2 and 4 are in A336375; 2 and 5 are in A336376; 3 and 7 are in A336377.

Crossrefs

Cf. A000040, A336366, A336375, A336376, A336377.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 2]] == 1 &]  (* A336374 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 2]] > 1 &]   (* A336375 *)
Prime[u]  (* A336376 *)
Prime[v]  (* A336377 *)
Showing 1-3 of 3 results.

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

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