A039710 -id:A039710 - cp's OEIS frontend

A039709 a(n) = n-th prime modulo 11.

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

Offset: 1

Clark Kimberling, Dec 11 1999

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A000040, A039703, A039705, A039710-A039715, A049084, A137977, A137978.

[p mod 11: p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 11, n=1..100); # Nathaniel Johnston, Jun 29 2011

Mod[Prime@ Range@ 86, 11] (* Robert G. Wilson v *)

primes(1000)%11 \\ Charles R Greathouse IV, Mar 13 2011

a(A049084(A137977(n-1))) = even; a(A049084(A137978(n-1))) = odd. - Reinhard Zumkeller, Feb 25 2008

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

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

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

A180217 a(n) = (n-th prime modulo 3) + (n-th prime modulo 4).

Original entry on oeis.org

4, 3, 3, 4, 5, 2, 3, 4, 5, 3, 4, 2, 3, 4, 5, 3, 5, 2, 4, 5, 2, 4, 5, 3, 2, 3, 4, 5, 2, 3, 4, 5, 3, 4, 3, 4, 2, 4, 5, 3, 5, 2, 5, 2, 3, 4, 4, 4, 5, 2, 3, 5, 2, 5, 3, 5, 3, 4, 2, 3, 4, 3, 4, 5, 2, 3, 4, 2, 5, 2, 3, 5, 4, 2, 4, 5, 3, 2, 3, 2, 5, 2, 5, 2, 4, 5, 3, 2, 3, 4, 5, 5, 4, 5, 4, 5, 3, 3, 4, 2, 4, 3

Offset: 1

Zak Seidov, Jan 16 2011

nonn

a(n) = 2 iff prime(n) == 1 (mod 12); a(n) = 2 for prime(n) = 13, 37, 61, 73, 97, 109, ... (A068228).
a(n) = 5 iff prime(n) == 11 (mod 12); a(n) = 5 for prime(n) = 11, 23, 47, 59, 71, 83, ... (A068231).
For n > 2, a(n) = 3 iff prime(n) == 5 (mod 12); a(n) = 3 for prime(n) = 5, 17, 29, 41, 53, 89, ... (A040117).
For n > 2, a(n) = 4 iff prime(n) == 7 (mod 12); a(n) = 4 for prime(n) = 7, 19, 31, 43, 67, 79, ... (A068229).

Equals A039701 + A039702.

Cf. A068228, A068231, A040117, A068229, A039710.

A180217:=func< n | p mod 3 + p mod 4 where p is NthPrime(n) >; [ A180217(n): n in [1..105] ]; // Klaus Brockhaus, Jan 18 2011

Mod[#,3]+Mod[#,4]&/@Prime[Range[110]] (* Harvey P. Dale, Nov 09 2011 *)

cp's OEIS Frontend

A039709 a(n) = n-th prime modulo 11.

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A242119 Primes modulo 18.

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

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Magma

Maple

Mathematica

PARI

Sage

Formula

A180217 a(n) = (n-th prime modulo 3) + (n-th prime modulo 4).

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