A102338 -id:A102338 - 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

A007811 Numbers k for which 10k+1, 10k+3, 10k+7 and 10k+9 are primes.

Original entry on oeis.org

1, 10, 19, 82, 148, 187, 208, 325, 346, 565, 943, 1300, 1564, 1573, 1606, 1804, 1891, 1942, 2101, 2227, 2530, 3172, 3484, 4378, 5134, 5533, 6298, 6721, 6949, 7222, 7726, 7969, 8104, 8272, 8881, 9784, 9913, 10111, 10984, 11653, 11929, 12220, 13546, 14416, 15727

Offset: 1

N. J. A. Sloane and J. H. Conway, Mar 15 1996

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A024912, A102338, A102342, A102700, A007530, A014561, A008471, A032352, A216292, A216293, A125855.

Cf. A010051, A245304, A245305.

a007811 n = a007811_list !! (n-1)
a007811_list = map (pred . head) $ filter (all (== 1) . map a010051') $
   iterate (zipWith (+) [10, 10, 10, 10]) [1, 3, 7, 9]
-- Reinhard Zumkeller, Jul 18 2014

[n: n in [0..10000] | forall{10*n+r: r in [1,3,7,9] | IsPrime(10*n+r)}]; // Bruno Berselli, Sep 04 2012

for n from 1 to 10000 do m := 10*n: if isprime(m+1) and isprime(m+3) and isprime(m+7) and isprime(m+9) then print(n); fi: od: quit

Select[ Range[ 1, 10000, 3 ], PrimeQ[ 10*#+1 ] && PrimeQ[ 10*#+3 ] && PrimeQ[ 10*#+7 ] && PrimeQ[ 10*#+9 ]& ]
Select[Range[15000], And @@ PrimeQ /@ ({1, 3, 7, 9} + 10#) &] (* Ray Chandler, Jan 12 2007 *)

p=2;q=3;r=5;forprime(s=7,1e5,if(s-p==8 && r-p==6 && q-p==2 && p%10==1, print1(p", ")); p=q;q=r;r=s) \\ Charles R Greathouse IV, Mar 21 2013

use ntheory ":all"; my @s = map { ($-1)/10 } sieve_prime_cluster(10,1e9, 2,6,8); say for @s; # _Dana Jacobsen, May 04 2017

a(n) = 3*A014561(n) + 1. - Zak Seidov, Sep 21 2009

A023238 Primes p such that 10*p + 3 is also prime.

Original entry on oeis.org

2, 5, 7, 11, 17, 19, 23, 29, 31, 37, 43, 59, 61, 67, 73, 101, 103, 109, 137, 149, 173, 191, 193, 197, 199, 211, 227, 229, 233, 239, 263, 269, 271, 283, 331, 337, 353, 359, 367, 373, 379, 383, 401, 409, 449, 467, 479, 499, 523, 541, 557, 569, 607, 613, 617, 647, 673, 683

Offset: 1

David W. Wilson

nonn

John Cerkan, Table of n, a(n) for n = 1..10000

Cf. A023239.

Subsequence of A102338.

[n: n in [0..1000] | IsPrime(n) and IsPrime(10*n+3)] // Vincenzo Librandi, Nov 20 2010

A023238:=n->`if`(isprime(n) and isprime(10*n+3), n, NULL): seq(A023238(n), n=1..10^3); # Wesley Ivan Hurt, Sep 08 2016

Select[Prime[Range[200]], PrimeQ[10# + 3] &] (* Alonso del Arte, Jun 24 2014 *)

A049508 Numbers k such that prime(k) == 3 (mod 10).

Original entry on oeis.org

2, 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, 227, 231

Offset: 1

J. Lowell

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

Cf. A000720, A030431, A102338.

Cf. A049509, A049510, A049511.

Select[Range[240], Mod[Prime[ # ], 10] == 3 &] (* Ray Chandler, Nov 07 2006 *)

a(n) = A000720(A030431(n)). - Ray Chandler, Nov 07 2006

Edited and extended by Ray Chandler, Nov 07 2006

A023269 Primes that remain prime through 2 iterations of function f(x) = 10x + 3.

Original entry on oeis.org

2, 7, 17, 19, 23, 37, 61, 67, 73, 101, 103, 173, 193, 233, 359, 383, 409, 479, 541, 557, 607, 613, 719, 809, 857, 997, 1013, 1033, 1109, 1117, 1237, 1297, 1361, 1459, 1531, 1549, 1699, 1823, 1871, 1979, 1999, 2069, 2131, 2161, 2347, 2377, 2399, 2447, 2663

Offset: 1

David W. Wilson

nonn

Primes p such that 10*p+3 and 100*p+33 are also primes. - Vincenzo Librandi, Aug 04 2010

John Cerkan, Table of n, a(n) for n = 1..10000

Subsequence of A023238 and of A102338.

[n: n in [1..100000] | IsPrime(n) and IsPrime(10*n+3) and IsPrime(100*n+33)] // Vincenzo Librandi, Aug 04 2010

Select[Prime@ Range@ 400, Times @@ Boole@ PrimeQ@ Rest@ NestList[10 # + 3 &, #, 2] > 0 &] (* Michael De Vlieger, Sep 16 2016 *)
Select[Prime[Range[500]],AllTrue[Rest[NestList[10#+3&,#,2]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 03 2018 *)

A153403 Numbers n such that 10*n+3 is not prime.

Original entry on oeis.org

3, 6, 9, 12, 13, 14, 15, 18, 20, 21, 24, 25, 27, 30, 32, 33, 34, 36, 39, 40, 41, 42, 45, 47, 48, 49, 51, 53, 54, 55, 57, 58, 60, 62, 63, 66, 69, 70, 71, 72, 75, 76, 78, 79, 80, 81, 83, 84, 87, 89, 90, 91, 92, 93, 94, 96, 97, 99, 100

Offset: 1

Vincenzo Librandi, Dec 25 2008

			Distribution of the terms in the following triangular array:
*;
*,*;
*,*,*;
*,*,6,*;
3,*,*,*,*;
*,*,*,*,14,*;
*,*,*,*,*,*,*;
*,*,*,15,*,*,*,*;
*,*,13,*,*,*,*,32,*;
6,*,*,*,*,27,*,*,*,*;
*,*,*,*,25,*,*,*,*,48,*; etc.
where * marks the non-integer values of (2*h*k + k + h - 1)/5 with n >= k >= 1. - _Vincenzo Librandi_, Jan 14 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A102338.

[n: n in [0..150] | not IsPrime(10*n + 3)]; // Vincenzo Librandi, Jan 14 2013

lst={};Do[p=10*n+3;If[ !PrimeQ[p],AppendTo[lst,n]],{n,0,6!}];lst (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *)
Select[Range[100],CompositeQ[10#+3]&] (* Harvey P. Dale, Jan 19 2025 *)

A102915 Numbers n such that n3 is prime and n is a multiple of 10.

Original entry on oeis.org

0, 10, 50, 110, 130, 200, 220, 250, 280, 290, 320, 380, 400, 460, 470, 490, 500, 530, 550, 590, 620, 670, 680, 710, 760, 770, 880, 910, 920, 940, 980, 1010, 1030, 1090, 1100, 1150, 1190, 1220, 1250, 1270, 1300, 1310, 1390, 1430, 1450, 1580, 1610, 1660, 1670, 1690, 1720, 1790, 1850, 1880

Offset: 1

Parthasarathy Nambi, Mar 01 2005

			If t=10, then t3 = 103 (prime).
If t=280, then t3 = 2803 (prime).
If t=490, then t3 = 4903 (prime).

Cf. A102338.

Select[10*Range[0,200],PrimeQ[10#+3]&] (* Harvey P. Dale, Mar 23 2015 *)

A126332 Numbers k such that 10k + 13 is prime.

Original entry on oeis.org

0, 1, 3, 4, 6, 7, 9, 10, 15, 16, 18, 21, 22, 25, 27, 28, 30, 34, 36, 37, 42, 43, 45, 49, 51, 55, 58, 60, 63, 64, 66, 67, 72, 73, 76, 81, 84, 85, 87, 94, 97, 100, 102, 105, 108, 109, 111, 114, 115, 118, 120, 121, 127, 129, 136, 141, 142, 144, 147, 148, 151, 153, 154, 157

Offset: 1

Parthasarathy Nambi, Mar 10 2007

			For k = 100, 10*k + 13 = 1013 (prime).

Cf. A102342, A126785.

[n: n in [0..1000] | IsPrime(10*n + 13)]; // Vincenzo Librandi, Nov 23 2010

Select[Range[0,157],PrimeQ[10#+13]&] (* James C. McMahon, Dec 25 2024 *)

is(n)=isprime(10*n+13) \\ Charles R Greathouse IV, Jun 13 2017

a(k) = A102338(k+1) - 1. - R. J. Mathar, Jul 08 2009

cp's OEIS Frontend

A030431 Primes of form 10n+3.

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A007811 Numbers k for which 10k+1, 10k+3, 10k+7 and 10k+9 are primes.

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A023238 Primes p such that 10*p + 3 is also prime.

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A049508 Numbers k such that prime(k) == 3 (mod 10).

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Mathematica

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A023269 Primes that remain prime through 2 iterations of function f(x) = 10x + 3.

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Magma

Mathematica

A153403 Numbers n such that 10*n+3 is not prime.

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Magma

Mathematica

A102915 Numbers n such that n3 is prime and n is a multiple of 10.

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Mathematica

A126332 Numbers k such that 10k + 13 is prime.

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