A045356 -id:A045356 - cp's OEIS frontend

A216057 a(n) = A045429(n) - A045356(n).

1, 6, 6, 6, 12, 12, 6, 6, 2, 4, -6, -6, 4, -4, 4, 4, 14, 24, 24, 24, 24, 14, 14, 24, 6, 12, 12, 6, 2, 4, -24, -24, -26, -34, -18, -6, 6, 4, 12, 24, 22, 14, 4, 12, 6, 24, 24, 34, 24, 32, 16, 14, 24, 24, 26, 32, 34, 26, 34, 14, 14, 6, -18, -18, 6, 4, -6, -8, -14

Offset: 1

Zak Seidov, Aug 31 2012

sign

Zak Seidov, Table of n, a(n) for n = 1..1000
Zak Seidov, Plot of terms up to a(1000) (gif image)
A. Granville and G. Martin, Prime number races, arXiv:math/0408319v1 [math.NT]
Eric Weisstein's World of Mathematics, Chebyshev Bias

Cf. A007350, A007351, A038691, A038698, A045356, A045429, A156749.

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

Original entry on oeis.org

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

A045429 Primes congruent to {1, 3} mod 5.

Original entry on oeis.org

3, 11, 13, 23, 31, 41, 43, 53, 61, 71, 73, 83, 101, 103, 113, 131, 151, 163, 173, 181, 191, 193, 211, 223, 233, 241, 251, 263, 271, 281, 283, 293, 311, 313, 331, 353, 373, 383, 401, 421, 431, 433, 443, 461, 463, 491, 503, 521, 523, 541, 563, 571, 593, 601, 613, 631, 641

Offset: 1

N. J. A. Sloane

A039703(A049084(a(n))) = odd; complement of A045356. - Reinhard Zumkeller, Feb 25 2008

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

Cf. A000040, A045415, A137978.

[ p: p in PrimesUpTo(600) | p mod 5 in {1,3} ]; // Vincenzo Librandi, Aug 13 2012

Select[Prime[Range[200]], MemberQ[{1, 3}, Mod[#, 5]] &] (* Vincenzo Librandi, Aug 13 2012 *)
Select[Prime[Range[200]], OddQ[Mod[#, 5]] &] (* Zak Seidov, Aug 31 2012 *)

A045370 Primes congruent to {0, 2, 4, 6} mod 7.

Original entry on oeis.org

2, 7, 11, 13, 23, 37, 41, 53, 67, 79, 83, 97, 107, 109, 137, 139, 149, 151, 163, 167, 179, 181, 191, 193, 223, 233, 251, 263, 277, 293, 307, 317, 331, 347, 349, 359, 373, 389, 401, 419, 431, 433, 443, 457, 461

Offset: 1

N. J. A. Sloane

A039705(A049084(a(n))) = even; complement of A045415. - Reinhard Zumkeller, Feb 25 2008

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

Cf. A045415, A045356, A137977.

[ p: p in PrimesUpTo(600) | p mod 7 in {0..6 by 2} ]; // Vincenzo Librandi, Aug 10 2012

Select[Prime[Range[300]],MemberQ[{0,2,4,6},Mod[#,7]]&] (* Vincenzo Librandi, Aug 10 2012 *)
Select[Prime[Range[110]], EvenQ[Mod[#, 7]] & ] (* Bruno Berselli, Aug 31 2012 *)

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 *)

A212719 Numbers n with property that the subset A039703(1..n) contains equal numbers of odd and even terms.

Original entry on oeis.org

2, 6, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 44, 48, 54, 56, 58, 60, 70, 72, 74, 76, 84, 86, 90, 100, 122, 124, 128, 130, 132, 134, 136, 138, 142, 144, 192, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 234, 236, 238, 240, 254, 256, 258, 282, 284, 286

Offset: 1

Zak Seidov, Aug 29 2012

nonn

It appears that the sequence is infinite and unbound.

Cf. A039703, A096629.
Cf. A045356 (primes congruent to {0,2,4} mod 5).
Cf. A045429 (primes congruent to {1,3} mod 5).

cp's OEIS Frontend

A216057 a(n) = A045429(n) - A045356(n).

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

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A045429 Primes congruent to {1, 3} mod 5.

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Magma

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A045370 Primes congruent to {0, 2, 4, 6} mod 7.

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Magma

Mathematica

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

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Magma

Mathematica

A212719 Numbers n with property that the subset A039703(1..n) contains equal numbers of odd and even terms.

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