A111223 -id:A111223 - cp's OEIS frontend

A023217 Primes p such that 5*p + 2 is also prime.

3, 7, 13, 19, 31, 61, 67, 73, 79, 97, 109, 151, 157, 181, 193, 199, 223, 313, 331, 349, 373, 397, 457, 487, 523, 541, 571, 577, 607, 613, 643, 661, 691, 709, 727, 739, 769, 811, 859, 919, 991, 997, 1021, 1033, 1039, 1069, 1087, 1129, 1171, 1201, 1213, 1249, 1279, 1321

Offset: 1

David W. Wilson

Except for the first term, all terms are congruent to 1 (mod 6). - John Cerkan, Sep 07 2016
Numbers k such that A280720(k) > 0. - Felix Fröhlich, Jan 07 2017
Intersection of A000040 and A111223. - Felix Fröhlich, Jan 07 2017

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

Cf. A000040, A111223, A280720. Subsequence of A111223.

[n: n in PrimesUpTo(400) | IsPrime(5*n+2)]; // Vincenzo Librandi, Nov 20 2010

A023217:=n->`if`(isprime(n) and isprime(5*n+2), n, NULL): seq(A023217(n), n=1..3*10^3); # Wesley Ivan Hurt, Sep 07 2016

Select[Prime[Range[200]], PrimeQ[5 # + 2] &] (* Vincenzo Librandi, May 20 2014 *)

is(n) = ispseudoprime(n) && ispseudoprime(5*n+2) \\ Felix Fröhlich, Jan 07 2017

A023283 Primes that remain prime through 3 iterations of function f(x) = 5x + 2.

Original entry on oeis.org

19, 373, 607, 1171, 1381, 1867, 2137, 2539, 3181, 4021, 5689, 5827, 5857, 6163, 7213, 7507, 11497, 12007, 13291, 13687, 14173, 15193, 16453, 21997, 22501, 24799, 25657, 28723, 31393, 31957, 32587, 35863, 40813, 42667, 42859, 43321, 43951, 45061, 45691

Offset: 1

David W. Wilson

nonn

Primes p such that 5*p+2, 25*p+12 and 125*p+62 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023217, A023252, and of A111223.

[n: n in [1..150000] | IsPrime(n) and IsPrime(5*n+2) and IsPrime(25*n+12) and IsPrime(125*n+62)] // Vincenzo Librandi, Aug 04 2010

Select[Prime@ Range@ 4800, Times @@ Boole@ PrimeQ@ Rest@ NestList[5 # + 2 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 20 2016 *)

a(n) == 1 (mod 6). - John Cerkan, Sep 20 2016

A023313 Primes that remain prime through 4 iterations of function f(x) = 5x + 2.

Original entry on oeis.org

373, 1171, 13687, 21997, 25657, 61603, 74413, 76471, 84199, 87181, 93487, 114691, 135859, 170761, 174877, 184333, 192979, 196177, 207931, 209743, 244219, 276229, 286687, 292561, 297811, 334603, 338893, 405037, 408361, 417097, 439141, 446323

Offset: 1

David W. Wilson

nonn

Primes p such that 5*p+2, 25*p+12, 125*p+62 and 625*p+312 are also primes. - Vincenzo Librandi, Aug 04 2010

Numbers k such that A280720(k) > 3. - Felix Fröhlich, Jan 07 2017

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

Cf. A280720. Subsequence of A023217, A023252, A023283, and A111223.

[n: n in [1..1000000] | IsPrime(n) and IsPrime(5*n+2) and IsPrime(25*n+12) and IsPrime(125*n+62) and IsPrime(625*n+312)]; // Vincenzo Librandi, Aug 04 2010

Select[Range[10^6], Times @@ Boole@ Map[PrimeQ, NestList[5 # + 2 &, #, 4]] == 1 &] (* Michael De Vlieger, Jan 09 2017 *)

a(n) == 31 or 37 (mod 42). - John Cerkan, Oct 07 2016

A023341 Primes that remain prime through 5 iterations of function f(x) = 5x + 2.

Original entry on oeis.org

135859, 174877, 192979, 244219, 292561, 679297, 842341, 964897, 1076029, 1470241, 1990579, 2004943, 2339263, 2615707, 2625577, 2633557, 2892277, 3003787, 3201901, 3758233, 4406797, 5065861, 5157547, 5390857, 5424961, 5546173, 5875369, 7746217

Offset: 1

David W. Wilson

nonn

Primes p such that 5*p+2, 25*p+12, 125*p+62, 625*p+312 and 3125*p+1562 are also primes. - Vincenzo Librandi, Aug 05 2010

Numbers k such that A280720(k) > 4. - Felix Fröhlich, Jan 07 2017

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

Subsequence of A023217, A023252, A023283, A023313, and A111223.

Cf. A280720.

[n: n in [1..10000000] | IsPrime(n) and IsPrime(5*n+2) and IsPrime(25*n+12) and IsPrime(125*n+62) and IsPrime(625*n+312) and IsPrime(3125*n+1562)] // Vincenzo Librandi, Aug 05 2010

p5Q[n_]:=And@@PrimeQ/@NestList[5#+2&,n,5]
Select[Prime[Range[550000]],p5Q]  (* Harvey P. Dale, Feb 17 2011 *)

a(n) == 31 (mod 42). - John Cerkan, Oct 17 2016

A107771 Numbers n such that 2n + 5 and 5n + 2 are primes.

Original entry on oeis.org

0, 1, 3, 7, 9, 13, 19, 21, 27, 31, 33, 39, 51, 61, 63, 67, 73, 79, 93, 97, 109, 111, 117, 123, 129, 151, 171, 177, 181, 187, 189, 217, 219, 237, 243, 247, 259, 297, 313, 319, 321, 327, 339, 357, 369, 373, 403, 417, 427, 441, 453, 457, 471, 483, 489, 493, 523, 529

Offset: 1

Zak Seidov, Mar 31 2006

nonn

Union of A089038 and A111223.

Except for the first, all terms == 1 or 3 (mod 6). - Robert Israel, Apr 02 2020

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A089038, A111223.

select(n -> isprime(2*n+5) and isprime(5*n+2), [0,seq(i,i=1..1000,2)]); # Robert Israel, Apr 02 2020

Reap[Do[If[PrimeQ[2*n+5]&&PrimeQ[5*n+2],Sow[n]],{n,0,600}]][[2,1]]

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A023217 Primes p such that 5*p + 2 is also prime.

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A023283 Primes that remain prime through 3 iterations of function f(x) = 5x + 2.

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A023313 Primes that remain prime through 4 iterations of function f(x) = 5x + 2.

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A023341 Primes that remain prime through 5 iterations of function f(x) = 5x + 2.

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A107771 Numbers n such that 2*n + 5 and 5*n + 2 are primes.

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A107771 Numbers n such that 2n + 5 and 5n + 2 are primes.