A039712 -id:A039712 - cp's OEIS frontend

A242119 Primes modulo 18.

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

A039711 a(n) = n-th prime modulo 13.

Original entry on oeis.org

2, 3, 5, 7, 11, 0, 4, 6, 10, 3, 5, 11, 2, 4, 8, 1, 7, 9, 2, 6, 8, 1, 5, 11, 6, 10, 12, 3, 5, 9, 10, 1, 7, 9, 6, 8, 1, 7, 11, 4, 10, 12, 9, 11, 2, 4, 3, 2, 6, 8, 12, 5, 7, 4, 10, 3, 9, 11, 4, 8, 10, 7, 8, 12, 1, 5, 6, 12, 9, 11, 2, 8, 3, 9, 2, 6, 12, 7, 11, 6

Offset: 1

Clark Kimberling

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

Cf. A039701-A039706, A038194, A007652, A039709, A039710, A039712-A039715.

[p mod(13): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 13, n=1..100); # Nathaniel Johnston, Jun 29 2011

Mod[ Prime@ Range@ 80, 13] (* Robert G. Wilson v, Mar 13 2011 *)

primes(1000)%13 \\ Charles R Greathouse IV, Mar 13 2011

[mod(p, 13) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ (13/2)*n. - Amiram Eldar, Dec 11 2024

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

A079950 Triangle of n-th prime modulo twice primes less n-th prime.

Original entry on oeis.org

2, 3, 3, 1, 5, 5, 3, 1, 7, 7, 3, 5, 1, 11, 11, 1, 1, 3, 13, 13, 13, 1, 5, 7, 3, 17, 17, 17, 3, 1, 9, 5, 19, 19, 19, 19, 3, 5, 3, 9, 1, 23, 23, 23, 23, 1, 5, 9, 1, 7, 3, 29, 29, 29, 29, 3, 1, 1, 3, 9, 5, 31, 31, 31, 31, 31, 1, 1, 7, 9, 15, 11, 3, 37, 37, 37, 37, 37, 1, 5, 1, 13, 19, 15, 7, 3, 41

Offset: 1

Reinhard Zumkeller, Jan 19 2003

The right border of the triangle are the primes: T(n,n)=A000040(n); T(n,1)=A039702(n), T(n,2)=A039704(n) for n>1, T(n,3)=A007652(n) for n>2, T(n,4)=A039712(n) for n>3;

			Triangle begins:
  2;
  3, 3;
  1, 5, 5;
  3, 1, 7,  7;
  3, 5, 1, 11, 11;
  1, 1, 3, 13, 13, 13;
  1, 5, 7,  3, 17, 17, 17;
  ...

Cf. A001747, A079951, A079952, A079953.

A079950 := proc(n,k)
    modp(ithprime(n),2*ithprime(k)) ;
end proc:
seq(seq(A079950(n,k),k=1..n),n=1..12) ; # R. J. Mathar, Sep 28 2017

T(n,k) = prime(n) % (2*prime(k));
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n,k), ", ")); print); \\ Michel Marcus, Sep 21 2017

T(n, k) = prime(n) mod 2*prime(k), 1<=k<=n.

cp's OEIS Frontend

A242119 Primes modulo 18.

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Magma

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Sage

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A039711 a(n) = n-th prime modulo 13.

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Magma

Maple

Mathematica

PARI

Sage

Formula

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

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Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Sage

Formula

A079950 Triangle of n-th prime modulo twice primes less n-th prime.

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Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

PARI

Formula