A039714 -id:A039714 - cp's OEIS frontend

A039715 Primes modulo 17.

2, 3, 5, 7, 11, 13, 0, 2, 6, 12, 14, 3, 7, 9, 13, 2, 8, 10, 16, 3, 5, 11, 15, 4, 12, 16, 1, 5, 7, 11, 8, 12, 1, 3, 13, 15, 4, 10, 14, 3, 9, 11, 4, 6, 10, 12, 7, 2, 6, 8, 12, 1, 3, 13, 2, 8, 14, 16, 5, 9, 11, 4, 1, 5, 7, 11, 8, 14, 7, 9, 13, 2, 10, 16, 5

Offset: 1

Clark Kimberling

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A039701-A039706, A038194, A007652, A039709-A039714.

[p mod(17): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 17, n=1..100); # Nathaniel Johnston, Jun 29 2011

Table[Mod[Prime[n], 17], {n, 100}] (* Nathaniel Johnston, Jun 29 2011 *)
Mod[Prime[Range[100]], 17] (* Vincenzo Librandi, May 06 2014 *)

primes(100)%17 \\ Charles R Greathouse IV, Apr 16 2012

[mod(p, 17) for p in primes(500)] # Bruno Berselli, May 05 2014

By the Prime Number Theorem in Arithmetic Progressions, all nonzero residue classes are equiprobable. In particular, Sum_{k=1..n} a(k) ~ 8.5n. - Charles R Greathouse IV, Apr 16 2012

A242119 Primes modulo 18.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 1, 5, 11, 13, 1, 5, 7, 11, 17, 5, 7, 13, 17, 1, 7, 11, 17, 7, 11, 13, 17, 1, 5, 1, 5, 11, 13, 5, 7, 13, 1, 5, 11, 17, 1, 11, 13, 17, 1, 13, 7, 11, 13, 17, 5, 7, 17, 5, 11, 17, 1, 7, 11, 13, 5, 1, 5, 7, 11, 7, 13, 5, 7, 11, 17, 7, 13, 1, 5

Offset: 1

Vincenzo Librandi, May 05 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. sequences of the type Primes mod k: A039701 (k=3), A039702 (k=4), A039703 (k=5), A039704 (k=6), A039705 (k=7), A039706 (k=8), A038194 (k=9), A007652 (k=10), A039709 (k=11), A039710 (k=12), A039711 (k=13), A039712 (k=14), A039713 (k=15), A039714 (k=16), A039715 (k=17), this sequence (k=18), A033633 (k=19), A242120(k=20), A242121 (k=21), A242122 (k=22), A229786 (k=23), A229787 (k=24), A242123 (k=25), A242124 (k=26), A242125 (k=27), A242126 (k=28), A242127 (k=29), A095959 (k=30), A110923 (k=100).

Magma
```
[p mod(18): p in PrimesUpTo(500)];
```
Mathematica
```
Mod[Prime[Range[100]], 18]
```

[mod(p, 18) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_{i=1..n} a(i) ~ 9n. The derivation is the same as in the formula in A039715. - Jerzy R Borysowicz, Apr 27 2022

A039713 a(n) = n-th prime modulo 15.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 2, 4, 8, 14, 1, 7, 11, 13, 2, 8, 14, 1, 7, 11, 13, 4, 8, 14, 7, 11, 13, 2, 4, 8, 7, 11, 2, 4, 14, 1, 7, 13, 2, 8, 14, 1, 11, 13, 2, 4, 1, 13, 2, 4, 8, 14, 1, 11, 2, 8, 14, 1, 7, 11, 13, 8, 7, 11, 13, 2, 1, 7, 2, 4, 8, 14, 7, 13, 4, 8, 14, 7

Offset: 1

Clark Kimberling

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A039701-A039706, A038194, A007652, A039709-A039712, A039714, A039715.

[p mod(15): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 15, n=1..100); # Nathaniel Johnston, Jun 29 2011

Table[Mod[Prime[n], 15], {n, 100}] (* Nathaniel Johnston, Jun 29 2011 *)
Mod[Prime[Range[100]], 15] (* Vincenzo Librandi, May 06 2014 *)

[mod(p, 15) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ (15/2)*n. - Amiram Eldar, Dec 12 2024

cp's OEIS Frontend

A039715 Primes modulo 17.

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A242119 Primes modulo 18.

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A039713 a(n) = n-th prime modulo 15.

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