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 1-10 of 15 results. Next

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 *)

A336367 Numbers k such that gcd(k, prime(k) + prime(k+1)) > 1.

Original entry on oeis.org

2, 3, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 93, 94, 96, 98, 100
Offset: 1

Views

Author

Clark Kimberling, Oct 04 2020

Keywords

Comments

Complement of A336366.

Examples

			In the following table, p(k) = A000040(k) = prime(k).
  k    p(k)   p(k)+p(k+1)   gcd
  1     2         5          1
  2     3         8          4
  3     5        12          3
  4     7        18          2
  5    11        24          1
  6    13        30          6
1 and 5 are in A336366; 2 and 3 are in this sequence; 2 and 11 are in A336368; 3 and 5 are in A336369.

Crossrefs

Cf. A000040, A336366, A336368, A336369.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 1]] == 1 &]  (* A336366 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 1]] > 1 &]   (* A336367 *)
Prime[u] (* A336368 *)
Prime[v] (* A336369 *)

A336368 Primes p(n) such that gcd(n, prime(n)+prime(n+1)) = 1.

Original entry on oeis.org

2, 11, 17, 23, 31, 41, 59, 67, 73, 83, 97, 109, 127, 157, 167, 179, 191, 211, 227, 233, 241, 277, 283, 331, 353, 367, 389, 401, 431, 439, 461, 467, 499, 509, 523, 547, 563, 587, 599, 607, 617, 631, 653, 661, 677, 691, 709, 727, 739, 751, 773, 797, 829, 859
Offset: 1

Views

Author

Clark Kimberling, Oct 04 2020

Keywords

Comments

This sequence and A336369 partition the set of primes.

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n)+p(n+1)   gcd
  1     2         5          1
  2     3         8          4
  3     5        12          3
  4     7        18          2
  5    11        24          1
  6    13        30          6
1 and 5 are in A336366; 2 and 3 are in A336367; 2 and 11 are in A336368; 3 and 5 are in A336369.

Crossrefs

Cf. A000040, A336366, A336367, A336369.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 1]] == 1 &]  (* A336366 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 1]] > 1 &]   (* A336367 *)
Prime[u] (* A336368 *)
Prime[v] (* A336369 *)

A336369 Primes p(n) such that gcd(n, prime(n)+prime(n+1)) > 1.

Original entry on oeis.org

3, 5, 7, 13, 19, 29, 37, 43, 47, 53, 61, 71, 79, 89, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 173, 181, 193, 197, 199, 223, 229, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 379, 383, 397, 409, 419, 421, 433
Offset: 1

Views

Author

Clark Kimberling, Oct 04 2020

Keywords

Comments

This sequence and A336368 partition the set of primes.

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n)+p(n+1)   gcd
  1     2         5          1
  2     3         8          4
  3     5        12          3
  4     7        18          2
  5    11        24          1
  6    13        30          6
1 and 5 are in A336366; 2 and 3 are in A336367; 2 and 11 are in A336368; 3 and 5 are in A336369.

Crossrefs

Cf. A000040, A336366, A336367, A336368.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 1]] == 1 &]  (* A336366 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 1]] > 1 &]   (* A336367 *)
Prime[u] (* A336368 *)
Prime[v] (* A336369 *)

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

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 *)

A336377 Primes p(n) such that gcd(n, prime(n)+prime(n+2)) > 1.

Original entry on oeis.org

3, 7, 13, 19, 23, 29, 37, 43, 53, 61, 71, 73, 79, 89, 97, 101, 107, 113, 131, 137, 139, 151, 163, 173, 181, 193, 197, 199, 223, 229, 233, 239, 251, 263, 269, 271, 281, 293, 311, 317, 337, 349, 359, 373, 379, 383, 397, 409, 421, 433, 443, 457, 463, 479, 491
Offset: 1

Views

Author

Clark Kimberling, Oct 06 2020

Keywords

Comments

This sequence and A336376 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, A336376.

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 *)

A336378 Numbers k such that gcd(k, prime(k-1) + prime(k+1)) = 1.

Original entry on oeis.org

2, 3, 7, 13, 17, 19, 23, 27, 29, 31, 37, 41, 43, 45, 47, 49, 53, 55, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 89, 91, 93, 95, 97, 101, 103, 107, 109, 111, 113, 117, 119, 121, 125, 127, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 157
Offset: 1

Views

Author

Clark Kimberling, Oct 06 2020

Keywords

Examples

			In the following table, p(k) = A000040(k) = prime(k).
  k    p(k)   p(k-1)+p(k+1)   gcd
  2     3          7           1
  3     5         10           1
  4     7         16           4
  5    11         20           5
  6    13         28           2
2 and 3 are in this sequence; 4 and 5 are in A336379; 3 and 5 are in A336380; 7 and 11 are in A336381.

Crossrefs

Cf. A000040, A336366, A336379, A336380, A336381.

Programs

  • Mathematica
    p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] == 1 &]  (* A336378 *)
v = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] > 1 &]   (* A336379 *)
Prime[u]  (* A336380 *)
Prime[v]  (* A336381 *)

Extensions

Offset corrected by Mohammed Yaseen, Jul 16 2023
Showing 1-10 of 15 results. Next

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

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