A023238 -id:A023238 - cp's OEIS frontend

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

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

A055782 Primes q of the form q = 10p + 3, where p is also prime.

Original entry on oeis.org

23, 53, 73, 113, 173, 193, 233, 293, 313, 373, 433, 593, 613, 673, 733, 1013, 1033, 1093, 1373, 1493, 1733, 1913, 1933, 1973, 1993, 2113, 2273, 2293, 2333, 2393, 2633, 2693, 2713, 2833, 3313, 3373, 3533, 3593, 3673, 3733, 3793, 3833, 4013, 4093, 4493

Offset: 1

Labos Elemer, Jul 13 2000

These primes correspond to resulting primes for A232210, when A232210(n)=1. - Vladimir Shevelev, Oct 16 2014

			5413 = 541*10 + 3, 3 appended to 541.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A005384, A005385, A023238. Apart from first term, same as A057667.

Select[Prime@ Range@ 630, PrimeQ[(# - 3)/10] &] (* Michael De Vlieger, Jul 14 2017 *)

lista(nn) = {forprime(p=2, nn, if (isprime(q=10*p+3), print1(q, ", ")););} \\ Michel Marcus, Oct 20 2014

a(n) = 10*A023238(n) + 3. - R. J. Mathar, Sep 21 2009

A023239 Primes p such that 10*p + 7 is also prime.

Original entry on oeis.org

3, 13, 19, 31, 61, 67, 79, 97, 109, 127, 163, 199, 223, 229, 241, 277, 283, 313, 367, 379, 421, 433, 439, 463, 487, 523, 541, 547, 571, 619, 631, 673, 691, 751, 757, 787, 811, 823, 829, 853, 859, 883, 937, 967, 1033, 1093, 1117, 1171, 1237, 1249, 1291, 1303, 1321

Offset: 1

David W. Wilson

nonn

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

Cf. A023238.

Subsequence of A102342.

[n: n in [0..1000] | IsPrime(n) and IsPrime(10*n+7)] // Vincenzo Librandi, Nov 20 2010

Select[Prime[Range[200]], PrimeQ[10# + 7] &] (* Alonso del Arte, Jun 24 2014 *)

a(n) == 1 (mod 6), for n > 1. - John Cerkan, Sep 12 2016

A066065 a(n) = smallest prime q such that in decimal notation the concatenation prime(n)q yields a prime ( = A066064(n)).

Original entry on oeis.org

3, 7, 3, 3, 3, 7, 3, 3, 3, 3, 3, 3, 11, 3, 23, 23, 3, 3, 3, 29, 3, 7, 11, 23, 7, 3, 3, 11, 3, 11, 7, 47, 3, 13, 3, 31, 31, 7, 29, 3, 11, 19, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 7, 11, 17, 3, 3, 3, 7, 11, 3, 11, 13, 23, 7, 23, 3, 3, 29, 13, 3, 3, 3, 3, 3, 3, 17, 19, 3, 3, 11, 7, 17, 7, 7, 71, 3, 37, 41

Offset: 1

Reinhard Zumkeller, Dec 01 2001

Conjecture: a(k) < prime(k) for k > 2.

a(n)=3 if and only if prime(n) is in A023238. - Robert Israel, Dec 27 2017

			A000040(13) = 41; for the first four primes 2, 3, 5 and 7 we get 412, 413, 415 and 417, which are all composite, but with the 5th prime we have 4111 = A066064(13), so a(13) = 11.

Robert Israel, Table of n, a(n) for n = 1..20000 (n=1..1000 from Harry J. Smith)

Cf. A000040, A023238, A066064.

N:= 100: # to get a(1)..a(N)
P:= Vector(N,ithprime):
A:= Vector(N):
q:= 2:
Agenda:= {$1..N}:
while Agenda <> {} do
  q:= nextprime(q);
  m:= 10^(ilog10(q)+1);
  L,Agenda:= selectremove(t -> isprime(P[t]*m+q), Agenda);
  A[convert(L,list)]:= q;
od:
convert(A,list); # Robert Israel, Dec 27 2017

a(n) = { my(p=prime(n)); forprime(q=3, oo, if(isprime(p*10^(logint(q,10)+1) + q), return(q))) } \\ Harry J. Smith, Nov 09 2009

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 *)

A105961 Primes p such that 20*p + 3 is prime.

Original entry on oeis.org

2, 5, 11, 13, 19, 23, 37, 41, 43, 53, 61, 71, 79, 83, 89, 103, 107, 127, 151, 167, 173, 179, 181, 191, 193, 197, 223, 229, 233, 239, 251, 281, 307, 313, 317, 349, 379, 421, 431, 433, 439, 443, 467, 487, 523, 569, 571, 587, 593, 607, 613, 617, 641, 653, 659

Offset: 1

Zak Seidov, May 05 2005

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A023238.

[p: p in PrimesUpTo(5000)|IsPrime(20*p+3)] // Vincenzo Librandi, Jan 30 2011

Select[Prime[Range[120]], PrimeQ[20#+3]&]

cp's OEIS Frontend

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

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A055782 Primes q of the form q = 10p + 3, where p is also prime.

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A023239 Primes p such that 10*p + 7 is also prime.

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Magma

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A066065 a(n) = smallest prime q such that in decimal notation the concatenation prime(n)q yields a prime ( = A066064(n)).

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Maple

PARI

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

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Author

Keywords

Comments

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Programs

Magma

Mathematica

A105961 Primes p such that 20*p + 3 is prime.

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Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica