A049508 -id:A049508 - cp's OEIS frontend

A030431 Primes of form 10n+3.

3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263, 283, 293, 313, 353, 373, 383, 433, 443, 463, 503, 523, 563, 593, 613, 643, 653, 673, 683, 733, 743, 773, 823, 853, 863, 883, 953, 983, 1013, 1033, 1063, 1093, 1103, 1123, 1153, 1163, 1193

Offset: 1

Warut Roonguthai

nonn

Also primes of form 5n+3.
Union of A132233, A132235, {3}. - Ray Chandler, Apr 07 2009
Primes p such that arithmetic mean of divisors of p^4 is an integer. There are 2 such sequences of primes, this one and A030430. - Ctibor O. Zizka, Oct 20 2009
5 is not quadratic residue of primes of this form. - Vincenzo Librandi, Jun 25 2014
Intersection of A000040 and A017305. - Iain Fox, Dec 30 2017

Michael B. Porter, Table of n, a(n) for n = 1..100000
A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004.

Cf. A045414, A049508, A053179, A102338.

Select[Prime@Range[200], Mod[ #, 10] == 3 &] (* Ray Chandler, Nov 07 2006 *)
Select[10 Range[0, 150] + 3, PrimeQ]  (* Harvey P. Dale, Apr 06 2011 *)

select(n->n%10==3, primes(500)) \\ Charles R Greathouse IV, Apr 29 2015

a(n) = 10*A102338(n) + 3.

Extended by Ray Chandler, Nov 07 2006

A049511 Numbers k such that prime(k) == 1 (mod 10).

Original entry on oeis.org

5, 11, 13, 18, 20, 26, 32, 36, 42, 43, 47, 53, 54, 58, 60, 64, 67, 79, 82, 83, 89, 94, 98, 100, 105, 110, 115, 116, 121, 125, 126, 133, 135, 141, 142, 152, 156, 160, 164, 167, 172, 173, 177, 178, 182, 190, 193, 194, 197, 202, 210, 212, 216, 218, 221, 230, 233

Offset: 1

N. J. A. Sloane

nonn

Also k for which prime(k) == 1 (mod 5). - Bruno Berselli, Mar 04 2016

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A000720, A024912, A030430, A081759.

Cf. A049508, A049509, A049510.

Select[Range[210], Mod[Prime[ # ], 10] == 1 &] (* Ray Chandler, Nov 07 2006 *)

isok(n) = !((prime(n)-1) % 10); \\ Michel Marcus, Mar 04 2016

[n for n in (1..300) if Mod(nth_prime(n), 10) == 1] # Bruno Berselli, Mar 04 2016

a(n) = A000720(A030430(n)). - Ray Chandler, Nov 07 2006

Extended by Ray Chandler, Nov 28 2003

Formula corrected by Zak Seidov, Sep 20 2011

A102338 Numbers k such that 10k+3 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 7, 8, 10, 11, 16, 17, 19, 22, 23, 26, 28, 29, 31, 35, 37, 38, 43, 44, 46, 50, 52, 56, 59, 61, 64, 65, 67, 68, 73, 74, 77, 82, 85, 86, 88, 95, 98, 101, 103, 106, 109, 110, 112, 115, 116, 119, 121, 122, 128, 130, 137, 142, 143, 145, 148, 149, 152, 154, 155

Offset: 1

Parthasarathy Nambi, Feb 20 2005

nonn

			For n=1, 10k+3 = 13 (prime).
For n=26, 10k+3 = 263 (prime).
For n=50, 10k+3 = 503 (prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A023238 (subsequence of primes), A030431, A049508.

[n: n in [0..1000]| IsPrime(10*n+3)]; // Vincenzo Librandi, Apr 06 2011

Select[Range[0, 160], PrimeQ[10# + 3] &] (* Ray Chandler, Nov 07 2006 *)

isok(n) = isprime(10*n+3); \\ Michel Marcus, Sep 08 2016

Edited and extended by Ray Chandler, Nov 07 2006

A049509 Numbers k such that prime(k) == 7 (mod 10).

Original entry on oeis.org

4, 7, 12, 15, 19, 25, 28, 31, 33, 37, 39, 45, 49, 55, 59, 63, 66, 68, 69, 73, 78, 88, 91, 93, 101, 102, 106, 107, 111, 113, 118, 123, 129, 134, 138, 139, 144, 148, 151, 154, 155, 159, 161, 163, 165, 168, 181, 184, 187, 195, 199, 203, 206, 211, 214, 217, 219, 225

Offset: 1

N. J. A. Sloane

nonn

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Cf. A000720, A030432, A102342.

Cf. A049508, A049510, A049511.

Select[Range[240], Mod[Prime[ # ], 10] == 7 &] (* Ray Chandler, Nov 07 2006 *)

a(n) = A000720(A030432(n)). - Ray Chandler, Nov 07 2006

Extended by Ray Chandler, Nov 07 2006

A049510 Numbers k such that prime(k) == 9 (mod 10).

Original entry on oeis.org

8, 10, 17, 22, 24, 29, 34, 35, 41, 46, 50, 52, 57, 70, 72, 75, 77, 80, 81, 85, 87, 92, 95, 97, 104, 109, 114, 120, 127, 128, 131, 136, 140, 145, 146, 149, 157, 158, 169, 171, 175, 176, 180, 186, 189, 201, 204, 205, 207, 209, 215, 222, 223, 226, 228, 232, 237, 239

Offset: 1

N. J. A. Sloane

nonn

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Cf. A000720, A030433, A102700.

Cf. A049508, A049509, A049511.

Select[Range[240], Mod[Prime[ # ], 10] == 9 &] (* Ray Chandler, Nov 07 2006 *)

a(n) = A000720(A030433(n)). - Ray Chandler, Nov 07 2006

Extended by Ray Chandler, Nov 07 2006

A244739 Numbers k such that (prime(k) mod 5) == 0 (mod 3).

Original entry on oeis.org

2, 3, 6, 9, 14, 16, 21, 23, 27, 30, 38, 40, 44, 48, 51, 56, 61, 62, 65, 71, 74, 76, 84, 86, 90, 96, 99, 103, 108, 112, 117, 119, 122, 124, 130, 132, 137, 143, 147, 150, 153, 162, 166, 170, 174, 179, 183, 185, 188, 191, 192, 196, 198, 200, 208, 213, 220, 224

Offset: 1

Clark Kimberling, Jul 05 2014

Every positive integer is in exactly one of the sequences A244739, A024707, A244741.

			n ... prime(n) mod 5 mod 3
1 ..... 2 ..... 2 ... 2
2 ..... 3 ..... 3 ... 0
3 ..... 5 ..... 0 ... 0
4 ..... 7 ..... 2 ... 2
5 ..... 11 .... 1 ... 1
6 ..... 13 .... 3 ... 0

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A039703, A244738, A024707, A244741, A244735. Essentially the same as A049508.

z = 300; u = Mod[Table[Mod[Prime[n], 5], {n, 1, z}], 3] (* A244738 *)
v1 = Flatten[Position[u, 0]]  (* A244739 *)
v2 = Flatten[Position[u, 1]]  (* A024707 *)
v3 = Flatten[Position[u, 2]]  (* A244741 *)

A240839 Both n and prime(n) are primes congruent to 3 (mod 10).

Original entry on oeis.org

23, 103, 293, 503, 823, 883, 953, 983, 1033, 1163, 1213, 1223, 1433, 1453, 1493, 1523, 1723, 1733, 1933, 1993, 2113, 2203, 2803, 2833, 2903, 3023, 3203, 3343, 3433, 3733, 3823, 3833, 4003, 4243, 4373, 4483, 4513, 4733, 4813, 4903, 4943, 4993, 5333, 5503, 5743, 6143, 6343, 6833, 7013

Offset: 1

Zak Seidov, Apr 13 2014

nonn

Intersection of A030431 and A049508.

			prime(23, 103, 293, 503, 823, 883, 953, 983, 1033, 1163)  =  (83, 563, 1913, 3593, 6323, 6863, 7523, 7753, 8233, 9403).

Zak Seidov, Table of n, a(n) for n = 1..469

Cf. A030431, A049508.

Intersection[A030431 = Select[Range[3, 1000003, 10], PrimeQ], PrimePi[A030431]] (* gives 469 terms for prime(n) up to 10^6 *)
Select[Prime[Range[50000]],Mod[#,10]==Mod[Prime[#],10]==3&] (* gives 3126 terms from the first 50000 primes *)(* Harvey P. Dale, Nov 29 2014 *)

s=[]; forprime(n=2, 8000, if(n%10==3 && prime(n)%10==3, s=concat(s, n))); s \\ Colin Barker, Apr 16 2014

cp's OEIS Frontend

A030431 Primes of form 10n+3.

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A049511 Numbers k such that prime(k) == 1 (mod 10).

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A102338 Numbers k such that 10k+3 is prime.

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A049509 Numbers k such that prime(k) == 7 (mod 10).

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A049510 Numbers k such that prime(k) == 9 (mod 10).

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A244739 Numbers k such that (prime(k) mod 5) == 0 (mod 3).

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A240839 Both n and prime(n) are primes congruent to 3 (mod 10).

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