A038194 -id:A038194 - cp's OEIS frontend

A039703 a(n) = n-th prime modulo 5.

2, 3, 0, 2, 1, 3, 2, 4, 3, 4, 1, 2, 1, 3, 2, 3, 4, 1, 2, 1, 3, 4, 3, 4, 2, 1, 3, 2, 4, 3, 2, 1, 2, 4, 4, 1, 2, 3, 2, 3, 4, 1, 1, 3, 2, 4, 1, 3, 2, 4, 3, 4, 1, 1, 2, 3, 4, 1, 2, 1, 3, 3, 2, 1, 3, 2, 1, 2, 2, 4, 3, 4, 2, 3, 4, 3, 4, 2, 1, 4, 4, 1, 1, 3, 4, 3, 4, 2, 1, 3, 2, 4, 2, 1, 4, 3, 4, 1, 3, 1, 2, 2, 3, 4, 1

Offset: 1

Clark Kimberling

a(A049084(A045356(n-1))) = even; a(A049084(A045429(n-1))) = odd. - Reinhard Zumkeller, Feb 25 2008

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

Cf. A000040, A010874, A039701, A039702, A039704-A039706, A038194, A007652, A039709-A039715.

[p mod 5: p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 5, n=1..105); # Nathaniel Johnston, Jun 29 2011

Table[Mod[Prime[n], 5], {n, 105}] (* Nathaniel Johnston, Jun 29 2011 *)
Mod[Prime[Range[100]], 5] (* Vincenzo Librandi, May 06 2014 *)

primes(105) % 5 \\ Zak Seidov, Apr 09 2013

Sum_k={1..n} a(k) ~ (5/2)*n. - Amiram Eldar, Dec 11 2024

A039715 Primes modulo 17.

Original entry on oeis.org

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

A039704 a(n) = n-th prime modulo 6.

Original entry on oeis.org

2, 3, 5, 1, 5, 1, 5, 1, 5, 5, 1, 1, 5, 1, 5, 5, 5, 1, 1, 5, 1, 1, 5, 5, 1, 5, 1, 5, 1, 5, 1, 5, 5, 1, 5, 1, 1, 1, 5, 5, 5, 1, 5, 1, 5, 1, 1, 1, 5, 1, 5, 5, 1, 5, 5, 5, 5, 1, 1, 5, 1, 5, 1, 5, 1, 5, 1, 1, 5, 1, 5, 5, 1, 1, 1, 5, 5, 1, 5, 1, 5, 1, 5, 1, 1, 5, 5, 1, 5, 1, 5, 5, 1, 5, 1, 5, 5, 5, 1, 1, 1, 5, 5, 5, 1

Offset: 1

Clark Kimberling

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

Cf. A000040, A039701-A039703, A039705, A039706, A038194, A007652, A039709-A039715.

[p mod 6: p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 6, n=1..105); # Nathaniel Johnston, Jun 29 2011

Table[Mod[Prime[n], 6], {n, 105}] (* Nathaniel Johnston, Jun 29 2011 *)
Mod[Prime[Range[100]], 6] (* Vincenzo Librandi, May 06 2014 *)

primes(105)%6 \\ Zak Seidov, Mar 25 2012

Sum_k={1..n} a(k) ~ 3*n. - Amiram Eldar, Dec 11 2024

A039705 a(n) = n-th prime modulo 7.

Original entry on oeis.org

2, 3, 5, 0, 4, 6, 3, 5, 2, 1, 3, 2, 6, 1, 5, 4, 3, 5, 4, 1, 3, 2, 6, 5, 6, 3, 5, 2, 4, 1, 1, 5, 4, 6, 2, 4, 3, 2, 6, 5, 4, 6, 2, 4, 1, 3, 1, 6, 3, 5, 2, 1, 3, 6, 5, 4, 3, 5, 4, 1, 3, 6, 6, 3, 5, 2, 2, 1, 4, 6, 3, 2, 3, 2, 1, 5, 4, 5, 2, 3, 6, 1, 4, 6, 5, 2, 1, 2, 6, 1, 5, 3, 4, 1, 2, 6, 5, 3, 5, 2, 1, 4, 3, 2, 4

Offset: 1

Clark Kimberling

a(A049084(A045370(n-1))) is even; a(A049084(A045415(n-1))) is odd. - Reinhard Zumkeller, Feb 25 2008

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

Cf. A039701-A039704, A039706, A038194, A007652, A039709-A039715.

[p mod(7): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 7, n=1..105); # Nathaniel Johnston, Jun 29 2011

Table[Mod[Prime[n], 7], {n, 105}] (* Nathaniel Johnston, Jun 29 2011 *)
Mod[Prime[Range[100]], 7] (* Vincenzo Librandi, May 06 2014 *)

primes(100)%7 \\ Charles R Greathouse IV, May 06 2014

Sum_k={1..n} a(k) ~ (7/2)*n. - Amiram Eldar, Dec 11 2024

A229875 Iterated sum-of-digits of palindromic prime; or digital root of palindromic prime.

Original entry on oeis.org

2, 3, 5, 7, 2, 2, 5, 7, 1, 2, 7, 2, 4, 5, 7, 1, 4, 5, 1, 2, 5, 7, 8, 7, 8, 1, 4, 5, 2, 7, 8, 4, 8, 7, 8, 5, 8, 1, 2, 2, 7, 1, 4, 5, 1, 2, 7, 8, 1, 4, 5, 8, 4, 4, 5, 8, 1, 4, 7, 8, 1, 5, 2, 5, 4, 7, 4, 5, 2, 8, 7, 1, 2, 1, 7, 2, 7, 2, 4, 8, 4, 2, 2, 2, 5, 4

Offset: 1

Shyam Sunder Gupta, Oct 02 2013

Integers with digital root 3, 6 or 9 are divisible by 3, so 3 is the only palindromic prime with digital root 3 and there are no palindromic primes with digital root 6 or 9.

			a(7)=5 because the 7th palindromic prime is 131 and 1+3+1 = 5.

Shyam Sunder Gupta, Table of n, a(n) for n = 1..5953

Cf. A002385, A010888, A038194.

t = {}; Do[z = n*10^(IntegerLength[n] - 1) + FromDigits@Rest@Reverse@IntegerDigits[n]; If[PrimeQ[z], AppendTo[t, Mod[z, 9]]], {n, 1, 99999}]; Insert[t, 2, 5]
Mod[#,9]&/@Select[Prime[Range[9000]],PalindromeQ] (* Harvey P. Dale, Mar 25 2025 *)

a(n) = A010888(A002385(n)). - R. J. Mathar, Sep 09 2015

A258876 Integers k such that both k and prime(k) have the same digital root.

Original entry on oeis.org

25, 32, 46, 56, 70, 88, 92, 98, 100, 113, 121, 130, 145, 146, 152, 175, 176, 182, 185, 206, 209, 212, 218, 227, 236, 239, 244, 248, 274, 293, 295, 301, 316, 317, 320, 323, 331, 338, 350, 352, 355, 362, 377, 386, 394, 397, 398, 406, 409, 413, 439

Offset: 1

Zak Seidov, Jun 13 2015

Integers k such that A010888(k) = A038194(k).

Conjecture: a(n) ~ 9n. - Charles R Greathouse IV, Jun 17 2015

			Both 25 and prime(25) = 97 have 7 for a digital root.
Both 32 and prime(32) = 131 have 5 for a digital root.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A010888, A038194.

Reap[Do[If[FixedPoint[Total[IntegerDigits[#]] &, n] == Mod[Prime[n], 9], Sow[n]], {n, 439}]][[2, 1]] (* Seidov *)
Select[Range[500], Mod[#, 9] == Mod[Prime[#], 9] &] (* Alonso del Arte, Jun 17 2015 *)

isok(n) = (n % 9) == (prime(n) % 9); \\ Michel Marcus, Jun 17 2015

n=0; forprime(p=2,1e4, if((p-n++)%9==0, print1(n", "))) \\ Charles R Greathouse IV, Jun 17 2015

A039710 a(n) = n-th prime modulo 12.

Original entry on oeis.org

2, 3, 5, 7, 11, 1, 5, 7, 11, 5, 7, 1, 5, 7, 11, 5, 11, 1, 7, 11, 1, 7, 11, 5, 1, 5, 7, 11, 1, 5, 7, 11, 5, 7, 5, 7, 1, 7, 11, 5, 11, 1, 11, 1, 5, 7, 7, 7, 11, 1, 5, 11, 1, 11, 5, 11, 5, 7, 1, 5, 7, 5, 7, 11, 1, 5, 7, 1, 11, 1, 5, 11, 7, 1, 7, 11, 5, 1, 5, 1, 11

Offset: 1

Clark Kimberling

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

Cf. A039701-A039706, A038194, A007652, A039709, A039711-A039715.

[p mod(12): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 12, n=1..100); # Nathaniel Johnston, Jun 29 2011

Table[Mod[Prime[n], 12], {n, 100}] (* Nathaniel Johnston, Jun 29 2011 *)
Mod[Prime[Range[100]], 12] (* Vincenzo Librandi, May 06 2014 *)

primes(100)%11 \\ Charles R Greathouse IV, Dec 12 2024

[mod(p, 12) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ 6*n. - Amiram Eldar, Dec 11 2024

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

A039712 a(n) = n-th prime modulo 14.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling

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

Cf. A039701-A039706, A038194, A007652, A039709-A039711, A039713-A039715.

[p mod(14): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 14, n=1..100); # Nathaniel Johnston, Jun 29 2011

Table[Mod[Prime[n], 14], {n, 100}] (* Nathaniel Johnston, Jun 29 2011 *)
Mod[Prime[Range[100]], 14] (* Vincenzo Librandi, May 06 2014 *)

[mod(p, 14) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_k={1..n} a(k) ~ 7*n. - Amiram Eldar, Dec 12 2024

cp's OEIS Frontend

A039703 a(n) = n-th prime modulo 5.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A039715 Primes modulo 17.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Sage

Formula

A242119 Primes modulo 18.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Sage

Formula

A039704 a(n) = n-th prime modulo 6.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A039705 a(n) = n-th prime modulo 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A229875 Iterated sum-of-digits of palindromic prime; or digital root of palindromic prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A258876 Integers k such that both k and prime(k) have the same digital root.

Views

Author

Keywords

Comments

Examples