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.

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 *)

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 *)

A355670 Numbers k such that A246600(k) < A000005(k).

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, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 55, 56, 57, 58, 60, 62, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 91, 92, 93, 94, 96
Offset: 1

Views

Author

Chai Wah Wu, Dec 19 2022

Keywords

Comments

Numbers k such that bitwise OR(k, d_1, d_2, ... d_m) > k where d_1, ..., d_m are the divisors of k.
Complement of A359080.
First 21 terms coincide with A336376.
A102554 is a subsequence; this sequence contains 1, 135, 175, 243, 343, 351, 363, ... which are not in A102554.

Crossrefs

Cf. A000005, A102553, A102554, A246600, A336375, A359080.

Programs

  • Python
    from itertools import count, islice
from operator import ior
from functools import reduce
from sympy import divisors
def A355670_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:n|reduce(ior,divisors(n,generator=True))>n,count(max(startvalue,1)))
A355670_list = list(islice(A355670_gen(), 20))
Showing 1-4 of 4 results.

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

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