A045370 -id:A045370 - cp's OEIS frontend

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

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

A045356 Primes congruent to {0, 2, 4} mod 5.

Original entry on oeis.org

2, 5, 7, 17, 19, 29, 37, 47, 59, 67, 79, 89, 97, 107, 109, 127, 137, 139, 149, 157, 167, 179, 197, 199, 227, 229, 239, 257, 269, 277, 307, 317, 337, 347, 349, 359, 367, 379, 389, 397, 409, 419, 439, 449, 457, 467

Offset: 1

N. J. A. Sloane

A039703(A049084(a(n))) = even; complement of A045429. - Reinhard Zumkeller, Feb 25 2008

R. Zumkeller, Table of n, a(n) for n = 1..1001

Cf. A045370, A045378, A137977.

[ p: p in PrimesUpTo(1000) | p mod 5 in {0, 2, 4} ]; // Vincenzo Librandi, Aug 07 2012

Select[Prime[Range[400]], MemberQ[{0, 2, 4}, Mod[#, 5]] &] (* Vincenzo Librandi, Aug 07 2012 *)
Select[Prime[Range[100]], EvenQ[Mod[#, 5]] &]  (* Zak Seidov, Aug 31 2012 *)
Select[Flatten[#+{0,2,4}&/@(5*Range[0,100])],PrimeQ] (* Harvey P. Dale, Sep 14 2019 *)

A045415 Primes congruent to {1, 3, 5} mod 7.

Original entry on oeis.org

3, 5, 17, 19, 29, 31, 43, 47, 59, 61, 71, 73, 89, 101, 103, 113, 127, 131, 157, 173, 197, 199, 211, 227, 229, 239, 241, 257, 269, 271, 281, 283, 311, 313, 337, 353, 367, 379, 383, 397, 409, 421, 439, 449, 463, 467

Offset: 1

N. J. A. Sloane

A039705(A049084(a(n))) = odd; complement of A045370. - Reinhard Zumkeller, Feb 25 2008

R. Zumkeller, Table of n, a(n) for n = 1..1001

Cf. A000040, A045429, A137978.

[ p: p in PrimesUpTo(600) | p mod 7 in {1,3,5} ]; // Vincenzo Librandi, Aug 12 2012

Select[Prime[Range[100]],MemberQ[{1,3,5},Mod[#,7]]&] (* Harvey P. Dale, May 15 2011 *)

A137977 Primes congruent to {0, 2, 4, 6, 8, 10} modulo 11.

Original entry on oeis.org

2, 11, 13, 17, 19, 37, 41, 43, 59, 61, 79, 83, 101, 103, 107, 109, 127, 131, 149, 151, 167, 173, 191, 193, 197, 211, 233, 239, 241, 257, 263, 277, 281, 283, 307, 347, 349, 367, 373, 389, 409, 431, 433, 439, 457, 461, 479, 499, 503, 521, 523, 541, 547, 563, 569

Offset: 1

Reinhard Zumkeller, Feb 25 2008

A039709(A049084(a(n))) = even; complement of A137978.

R. Zumkeller, Table of n, a(n) for n = 1..1001

Cf. A000040, A045370, A045356.

[p: p in PrimesUpTo(600) | p mod 11 in [0..10 by 2]]; // Vincenzo Librandi, Aug 15 2012

Select[Prime[Range[200]], MemberQ[{0, 2, 4, 6, 8, 10}, Mod[#, 11]] &] (* Vincenzo Librandi, Aug 15 2012 *)
Select[Prime[Range[110]], EvenQ[Mod[#, 11]] &] (* Bruno Berselli, Aug 31 2012 *)

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A045356 Primes congruent to {0, 2, 4} mod 5.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

A045415 Primes congruent to {1, 3, 5} mod 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

A137977 Primes congruent to {0, 2, 4, 6, 8, 10} modulo 11.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica