A039705 -id:A039705 - cp's OEIS frontend

A039706 a(n) = n-th prime modulo 8.

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

Offset: 1

Clark Kimberling

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

Cf. A039701-A039705, A038194, A007652, A039709-A039715.

[p mod(8): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 8, n=1..105); # Nathaniel Johnston, Jun 29 2011

Table[Mod[Prime[n], 8], {n, 105}] (* Nathaniel Johnston, Jun 29 2011 *)
Mod[Prime[Range[100]], 8] (* Vincenzo Librandi, May 06 2014 *)

primes(100)%8 \\ Charles R Greathouse IV, May 06 2014

Sum_k={1..n} a(k) ~ 4*n. - Amiram Eldar, Dec 11 2024

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

Original entry on oeis.org

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

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

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 *)

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 *)

A103568 Sum of the (primes > 5 modulo 7).

Original entry on oeis.org

0, 4, 10, 13, 18, 20, 21, 24, 26, 32, 33, 38, 42, 45, 50, 54, 55, 58, 60, 66, 71, 77, 80, 85, 87, 91, 92, 93, 98, 102, 108, 110, 114, 117, 119, 125, 130, 134, 140, 142, 146, 147, 150, 151, 157, 160, 165, 167, 168, 171, 177, 182, 186, 189, 194, 198, 199, 202, 208, 214

Offset: 1

Roger L. Bagula, Mar 23 2005

Cf. A039705, A103566-A103567, A103569-A103572.

a = Table[Sum[Mod[Prime[i + 3], 7], {i, 1, n}], {n, 1, 200}]

a(n+1)-a(n) = A039705(n+4).

A122601 a(n)=(n-th prime +1) modulo 7.

Original entry on oeis.org

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

Offset: 1

Zak Seidov, Sep 24 2006

nonn

a(n)=1 only for n=4; frequences f(m) of other values are almost equal, e.g., for n=1..1000, f(m=0..6): 166,1,165,166,168,164,170.

Cf. A039705.

Mathematica
```
Table[Mod[(Prime[n]+1),7],{n,1000}]
```

a(n)= (A039705(n)+1) mod 7

A252728 Numbers k such that exactly 5 consecutive primes starting with prime(k) are congruent to the same value modulo 7.

Original entry on oeis.org

70872, 191056, 204048, 215955, 216351, 251872, 266249, 346159, 431099, 433456, 443366, 461372, 517528, 654361, 664677, 793519, 841521, 865347, 904987, 918479, 1056902, 1060733, 1063487, 1134245, 1140824, 1158526

Offset: 1

Zak Seidov, Feb 16 2015

nonn

Or, numbers k such A039705(k) = ... = A039705(k+4), but not A039705(k+5).

			k=70872, {A000040(k), ..., A000040(k+4)} = {894287, 894301, 894329, 894343, 894371} == 2 (mod 7).

Zak Seidov, Table of n, a(n) for n = 1..300

Cf. A000040, A039705.

cp's OEIS Frontend

A039706 a(n) = n-th prime modulo 8.

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

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A242119 Primes modulo 18.

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

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PARI

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

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Magma

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

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Magma

Mathematica

A103568 Sum of the (primes > 5 modulo 7).

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Programs

Mathematica

Formula

A122601 a(n)=(n-th prime +1) modulo 7.

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