A045415 -id:A045415 - 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

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 *)

A137978 Primes congruent to {1, 3, 5, 7, 9} modulo 11.

Original entry on oeis.org

3, 5, 7, 23, 29, 31, 47, 53, 67, 71, 73, 89, 97, 113, 137, 139, 157, 163, 179, 181, 199, 223, 227, 229, 251, 269, 271, 293, 311, 313, 317, 331, 337, 353, 359, 379, 383, 397, 401, 419, 421, 443, 449, 463, 467, 487, 491, 509, 557, 577, 599, 601, 617, 619, 641

Offset: 1

Reinhard Zumkeller, Feb 25 2008

nonn

A039709(A049084(a(n))) = odd; complement of A137977.

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

Cf. A045415, A045429.

[ p: p in PrimesUpTo(740) | p mod 11 in {1, 3, 5, 7, 9} ] // Vincenzo Librandi, Jan 25 2011

Select[Flatten[# + {1, 3, 5, 7, 9}&/@(11Range[0, 80])], PrimeQ] (* Harvey P. Dale, Jan 15 2011 *)

cp's OEIS Frontend

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

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

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

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A137978 Primes congruent to {1, 3, 5, 7, 9} modulo 11.

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