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 1-6 of 6 results.

A030432 Primes of form 10n+7.

Original entry on oeis.org

7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277, 307, 317, 337, 347, 367, 397, 457, 467, 487, 547, 557, 577, 587, 607, 617, 647, 677, 727, 757, 787, 797, 827, 857, 877, 887, 907, 937, 947, 967, 977, 997, 1087, 1097, 1117, 1187, 1217, 1237
Offset: 1

Views

Author

Warut Roonguthai

Keywords

Comments

Union of A132231 and A039949. - Ray Chandler, Apr 07 2009
5 is not quadratic residue of primes of this form. - Vincenzo Librandi, Jun 25 2014
Also primes of the form 5n+2 with positive n. - Danny Rorabaugh, Feb 20 2016
Intersection of A000040 and A017353. - Iain Fox, Dec 30 2017

Links

Crossrefs

Cf. A030430 (10n+1), A030431 (10n+3), A030433 (10n+9).
Cf. A045357, A045380, A049509, A102342.

Programs

  • Magma
    [n: n in [7..1240 by 10] | IsPrime(n)]; // Bruno Berselli, Apr 06 2011
  • Mathematica
    Select[Prime@Range[210], Mod[ #, 10] == 7 &] (* Ray Chandler, Nov 07 2006 *)
  • PARI
    is(n)=n%10==7 && isprime(n) \\ Charles R Greathouse IV, Jul 01 2013
  • PARI
    lista(nn) = forprime(p=7, nn, if(p%10==7, print1(p, ", "))) \\ Iain Fox, Dec 30 2017
  • Sage
    [10*n+7 for n in range(124) if is_prime(10*n+7)] # Danny Rorabaugh, Feb 20 2016

Formula

a(n) = 10*A102342(n) + 7.
a(n) ~ 4n log n. - Charles R Greathouse IV, Jul 01 2013

Extensions

Extended by Ray Chandler, Nov 07 2006

A102342 Numbers k such that 10k + 7 is prime.

Original entry on oeis.org

0, 1, 3, 4, 6, 9, 10, 12, 13, 15, 16, 19, 22, 25, 27, 30, 31, 33, 34, 36, 39, 45, 46, 48, 54, 55, 57, 58, 60, 61, 64, 67, 72, 75, 78, 79, 82, 85, 87, 88, 90, 93, 94, 96, 97, 99, 108, 109, 111, 118, 121, 123, 127, 129, 130, 132, 136, 142, 144, 148, 156, 159, 160, 162, 163
Offset: 1

Views

Author

Parthasarathy Nambi, Feb 20 2005

Keywords

Examples

			10*1 + 7 = 17 (prime);
10*48 + 7 = 487 (prime);
10*99 + 7 = 997 (prime).

Crossrefs

Cf. A030432, A049509.

Programs

Extensions

Edited and extended by Ray Chandler, Nov 07 2006

A049511 Numbers k such that prime(k) == 1 (mod 10).

Original entry on oeis.org

5, 11, 13, 18, 20, 26, 32, 36, 42, 43, 47, 53, 54, 58, 60, 64, 67, 79, 82, 83, 89, 94, 98, 100, 105, 110, 115, 116, 121, 125, 126, 133, 135, 141, 142, 152, 156, 160, 164, 167, 172, 173, 177, 178, 182, 190, 193, 194, 197, 202, 210, 212, 216, 218, 221, 230, 233
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Also k for which prime(k) == 1 (mod 5). - Bruno Berselli, Mar 04 2016
The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Links

Crossrefs

Cf. A000720, A024912, A030430, A081759.
Cf. A049508, A049509, A049510.

Programs

  • Mathematica
    Select[Range[210], Mod[Prime[ # ], 10] == 1 &] (* Ray Chandler, Nov 07 2006 *)
  • PARI
    isok(n) = !((prime(n)-1) % 10); \\ Michel Marcus, Mar 04 2016
  • Sage
    [n for n in (1..300) if Mod(nth_prime(n), 10) == 1] # Bruno Berselli, Mar 04 2016

Formula

a(n) = A000720(A030430(n)). - Ray Chandler, Nov 07 2006

Extensions

Extended by Ray Chandler, Nov 28 2003
Formula corrected by Zak Seidov, Sep 20 2011

A049508 Numbers k such that prime(k) == 3 (mod 10).

Original entry on oeis.org

2, 6, 9, 14, 16, 21, 23, 27, 30, 38, 40, 44, 48, 51, 56, 61, 62, 65, 71, 74, 76, 84, 86, 90, 96, 99, 103, 108, 112, 117, 119, 122, 124, 130, 132, 137, 143, 147, 150, 153, 162, 166, 170, 174, 179, 183, 185, 188, 191, 192, 196, 198, 200, 208, 213, 220, 224, 227, 231
Offset: 1

Views

Author

J. Lowell

Keywords

Comments

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Crossrefs

Cf. A000720, A030431, A102338.
Cf. A049509, A049510, A049511.

Programs

  • Mathematica
    Select[Range[240], Mod[Prime[ # ], 10] == 3 &] (* Ray Chandler, Nov 07 2006 *)

Formula

a(n) = A000720(A030431(n)). - Ray Chandler, Nov 07 2006

Extensions

Edited and extended by Ray Chandler, Nov 07 2006

A049510 Numbers k such that prime(k) == 9 (mod 10).

Original entry on oeis.org

8, 10, 17, 22, 24, 29, 34, 35, 41, 46, 50, 52, 57, 70, 72, 75, 77, 80, 81, 85, 87, 92, 95, 97, 104, 109, 114, 120, 127, 128, 131, 136, 140, 145, 146, 149, 157, 158, 169, 171, 175, 176, 180, 186, 189, 201, 204, 205, 207, 209, 215, 222, 223, 226, 228, 232, 237, 239
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Crossrefs

Cf. A000720, A030433, A102700.
Cf. A049508, A049509, A049511.

Programs

  • Mathematica
    Select[Range[240], Mod[Prime[ # ], 10] == 9 &] (* Ray Chandler, Nov 07 2006 *)

Formula

a(n) = A000720(A030433(n)). - Ray Chandler, Nov 07 2006

Extensions

Extended by Ray Chandler, Nov 07 2006

A244741 Numbers k such that (prime(k) mod 5) == 2 (mod 3).

Original entry on oeis.org

1, 4, 7, 12, 15, 19, 25, 28, 31, 33, 37, 39, 45, 49, 55, 59, 63, 66, 68, 69, 73, 78, 88, 91, 93, 101, 102, 106, 107, 111, 113, 118, 123, 129, 134, 138, 139, 144, 148, 151, 154, 155, 159, 161, 163, 165, 168, 181, 184, 187, 195, 199, 203, 206, 211, 214, 217
Offset: 1

Views

Author

Clark Kimberling, Jul 05 2014

Keywords

Comments

Every positive integer is in exactly one of the sequences A244739, A024707, A244741.

Examples

			n ... prime(n) mod 5 mod 3
1 ..... 2 ..... 2 ... 2
2 ..... 3 ..... 3 ... 0
3 ..... 5 ..... 0 ... 0
4 ..... 7 ..... 2 ... 2
5 ..... 11 .... 1 ... 1
6 ..... 13 .... 3 ... 0

Links

Crossrefs

Cf. A039703, A244738, A244739, A024707, A244735. Essentially the same as A049509.

Programs

  • Maple
    A244741:=n->`if`(((ithprime(n) mod 5) mod 3) = 2, n, NULL): seq(A244741(n), n=1..250); # Wesley Ivan Hurt, Jul 06 2014
  • Mathematica
    z = 300; u = Mod[Table[Mod[Prime[n], 5], {n, 1, z}], 3] (* A244738 *)
v1 = Flatten[Position[u, 0]]  (* A244739 *)
v2 = Flatten[Position[u, 1]]  (* A024707 *)
v3 = Flatten[Position[u, 2]]  (* A244741 *)
Showing 1-6 of 6 results.

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

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