A242119 -id:A242119 - cp's OEIS frontend

A110923 Final two digits of prime(n), with leading zero omitted.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 1, 3, 7, 9, 13, 27, 31, 37, 39, 49, 51, 57, 63, 67, 73, 79, 81, 91, 93, 97, 99, 11, 23, 27, 29, 33, 39, 41, 51, 57, 63, 69, 71, 77, 81, 83, 93, 7, 11, 13, 17, 31, 37

Offset: 1

Paolo P. Lava, Sep 23 2005

Primes modulo 100.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Index entries for sequences related to final digits of numbers.

Cf. A007652, A242119.

[p mod(100): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 07 2014

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

Table[Mod[Prime[n], 100], {n, 100}] (* Ray Chandler, Oct 01 2005 *)
Mod[Prime[Range[100]], 100] (* Vincenzo Librandi, May 07 2014 *)

[mod(p, 100) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ 50*n. - Amiram Eldar, Dec 13 2024

Edited, corrected and extended by Ray Chandler, Oct 01 2005

A242125 a(n) = n-th prime modulo 27.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 2, 4, 10, 14, 16, 20, 26, 5, 7, 13, 17, 19, 25, 2, 8, 16, 20, 22, 26, 1, 5, 19, 23, 2, 4, 14, 16, 22, 1, 5, 11, 17, 19, 2, 4, 8, 10, 22, 7, 11, 13, 17, 23, 25, 8, 14, 20, 26, 1, 7, 11, 13, 23, 10, 14, 16, 20, 7, 13, 23, 25, 2, 8

Offset: 1

Vincenzo Librandi, May 05 2014

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

Cf. similar sequences listed in A242119.

Magma
```
[p mod(27): p in PrimesUpTo(500)];
```
Mathematica
```
Mod[Prime[Range[100]], 27]
```

[mod(p, 27) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ (27/2)*n. - Amiram Eldar, Dec 12 2024

A033633 a(n) = n-th prime modulo 19.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 0, 4, 10, 12, 18, 3, 5, 9, 15, 2, 4, 10, 14, 16, 3, 7, 13, 2, 6, 8, 12, 14, 18, 13, 17, 4, 6, 16, 18, 5, 11, 15, 2, 8, 10, 1, 3, 7, 9, 2, 14, 18, 1, 5, 11, 13, 4, 10, 16, 3, 5, 11, 15, 17, 8, 3, 7, 9, 13, 8, 14, 5, 7, 11, 17, 6, 12, 18, 3, 9, 17, 2, 10

Offset: 1

Armand Turpel (armand_t(AT)yahoo.com)

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

Cf. similar sequences listed in A242119.

[p mod(19): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 07 2014

Mod[Prime[Range[100]], 19] (* Vincenzo Librandi, May 07 2014 *)

a(n) = A000040(n) mod 19.

Sum_k={1..n} a(k) ~ (19/2)*n. - Amiram Eldar, Dec 12 2024

A095959 a(n) = n-th prime modulo 30.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 1, 7, 11, 13, 17, 23, 29, 1, 7, 11, 13, 19, 23, 29, 7, 11, 13, 17, 19, 23, 7, 11, 17, 19, 29, 1, 7, 13, 17, 23, 29, 1, 11, 13, 17, 19, 1, 13, 17, 19, 23, 29, 1, 11, 17, 23, 29, 1, 7, 11, 13, 23, 7, 11, 13, 17, 1, 7, 17, 19, 23, 29, 7, 13, 19

Offset: 1

Reinhard Zumkeller, Jul 14 2004

A002110(3) = 2*3*5 = 30; range for n>3: {1,7,11,13,17,19,23,29} of size 8 = A000720(30) - #{2,3,5} + #{1} = 10 - 3 + 1 = A000010(30).

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

Cf. similar sequences listed in A242119.

Cf. A000010, A000720, A002110.

[p mod(30): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 07 2014

Mod[Prime[Range[80]], 30] (* Harvey P. Dale, Jul 21 2013 *)

Sum_k={1..n} a(k) ~ 15*n. - Amiram Eldar, Dec 13 2024

A229786 a(n) = n-th prime modulo 23.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 0, 6, 8, 14, 18, 20, 1, 7, 13, 15, 21, 2, 4, 10, 14, 20, 5, 9, 11, 15, 17, 21, 12, 16, 22, 1, 11, 13, 19, 2, 6, 12, 18, 20, 7, 9, 13, 15, 4, 16, 20, 22, 3, 9, 11, 21, 4, 10, 16, 18, 1, 5, 7, 17, 8, 12, 14, 18, 9, 15, 2, 4, 8, 14, 22, 5, 11, 15, 21, 6, 10, 18, 5, 7, 17, 19, 2, 6, 12, 20, 1, 3, 7, 19, 4, 8, 16, 20, 3, 15, 17, 12, 18, 5, 11, 17, 19, 2, 12, 18, 1, 3, 9, 15, 19, 21

Offset: 1

Freimut Marschner, Sep 29 2013

The formula k(n,p)=p mod n classifies prime numbers p(A000040) with n(A000027) in classes k, here n=23. Other examples for n=2,3,4,... are in the cross reference. Another description of this sequence is a(n) = n-th prime modulo 23 or Prime(n) mod 23.

Freimut Marschner, Table of n, a(n) for n = 1..1900

Cf. similar sequences listed in A242119.

[p mod(23): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 07 2014

Mod[Prime[Range[100]], 23] (* Vincenzo Librandi, May 07 2014 *)

k(n,p) = p mod n.

Sum_k={1..n} a(k) ~ (23/2)*n. - Amiram Eldar, Dec 12 2024

A229787 a(n) = n-th prime modulo 24.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 5, 7, 13, 17, 19, 23, 5, 11, 13, 19, 23, 1, 7, 11, 17, 1, 5, 7, 11, 13, 17, 7, 11, 17, 19, 5, 7, 13, 19, 23, 5, 11, 13, 23, 1, 5, 7, 19, 7, 11, 13, 17, 23, 1, 11, 17, 23, 5, 7, 13, 17, 19, 5, 19, 23, 1, 5, 19, 1, 11, 13, 17, 23, 7, 13, 19, 23, 5, 13, 17, 1, 11, 13, 23, 1, 7

Offset: 1

Freimut Marschner, Sep 29 2013

Freimut Marschner, Table of n, a(n) for n = 1..1900

Cf. similar sequences listed in A242119.

[p mod(24): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 07 2014

Mod[Prime[Range[100]], 24] (* Vincenzo Librandi, May 07 2014 *)

a(n) = prime(n) % 24; \\ Joerg Arndt, Oct 01 2013

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

A242120 a(n) = n-th prime modulo 20.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 3, 9, 11, 17, 1, 3, 7, 13, 19, 1, 7, 11, 13, 19, 3, 9, 17, 1, 3, 7, 9, 13, 7, 11, 17, 19, 9, 11, 17, 3, 7, 13, 19, 1, 11, 13, 17, 19, 11, 3, 7, 9, 13, 19, 1, 11, 17, 3, 9, 11, 17, 1, 3, 13, 7, 11, 13, 17, 11, 17, 7, 9, 13, 19, 7

Offset: 1

Vincenzo Librandi, May 05 2014

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

Cf. similar sequences listed in A242119.

Magma
```
[p mod(20): p in PrimesUpTo(500)];
```
Mathematica
```
Mod[Prime[Range[100]], 20]
```

[mod(p, 20) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ 10*n. - Amiram Eldar, Dec 12 2024

A242121 a(n) = n-th prime modulo 21.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 2, 8, 10, 16, 20, 1, 5, 11, 17, 19, 4, 8, 10, 16, 20, 5, 13, 17, 19, 2, 4, 8, 1, 5, 11, 13, 2, 4, 10, 16, 20, 5, 11, 13, 2, 4, 8, 10, 1, 13, 17, 19, 2, 8, 10, 20, 5, 11, 17, 19, 4, 8, 10, 20, 13, 17, 19, 2, 16, 1, 11, 13, 17, 2, 10

Offset: 1

Vincenzo Librandi, May 05 2014

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

Cf. similar sequences listed in A242119.

Magma
```
[p mod(21): p in PrimesUpTo(500)];
```
Mathematica
```
Mod[Prime[Range[100]], 21]
```

a(n) = prime(n) % 21; \\ Michel Marcus, May 05 2014

[mod(p, 21) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ (21/2)*n. - Amiram Eldar, Dec 12 2024

A242122 a(n) = n-th prime modulo 22.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 1, 7, 9, 15, 19, 21, 3, 9, 15, 17, 1, 5, 7, 13, 17, 1, 9, 13, 15, 19, 21, 3, 17, 21, 5, 7, 17, 19, 3, 9, 13, 19, 3, 5, 15, 17, 21, 1, 13, 3, 7, 9, 13, 19, 21, 9, 15, 21, 5, 7, 13, 17, 19, 7, 21, 3, 5, 9, 1, 7, 17, 19, 1, 7, 15

Offset: 1

Vincenzo Librandi, May 05 2014

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

Cf. similar sequences listed in A242119.

Magma
```
[p mod(22): p in PrimesUpTo(500)];
```
Mathematica
```
Mod[Prime[Range[100]], 22]
```

[mod(p, 22) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ 11*n. - Amiram Eldar, Dec 12 2024

A242123 a(n) = n-th prime modulo 25.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 4, 6, 12, 16, 18, 22, 3, 9, 11, 17, 21, 23, 4, 8, 14, 22, 1, 3, 7, 9, 13, 2, 6, 12, 14, 24, 1, 7, 13, 17, 23, 4, 6, 16, 18, 22, 24, 11, 23, 2, 4, 8, 14, 16, 1, 7, 13, 19, 21, 2, 6, 8, 18, 7, 11, 13, 17, 6, 12, 22, 24, 3, 9, 17

Offset: 1

Vincenzo Librandi, May 05 2014

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

Cf. similar sequences listed in A242119.

Magma
```
[p mod(25): p in PrimesUpTo(500)];
```
Mathematica
```
Mod[Prime[Range[100]], 25]
```

a(n) = prime(n) % 25; \\ Michel Marcus, May 05 2014

[mod(p, 25) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ (25/2)*n. - Amiram Eldar, Dec 12 2024

cp's OEIS Frontend

A110923 Final two digits of prime(n), with leading zero omitted.

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A242125 a(n) = n-th prime modulo 27.

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A033633 a(n) = n-th prime modulo 19.

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A095959 a(n) = n-th prime modulo 30.

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A229786 a(n) = n-th prime modulo 23.

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Magma

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A229787 a(n) = n-th prime modulo 24.

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A242120 a(n) = n-th prime modulo 20.

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Magma

Mathematica

Sage

Formula