A023207 -id:A023207 - cp's OEIS frontend

A171517 Primes p such that 2*p+11 is prime.

3, 13, 31, 43, 73, 109, 151, 163, 181, 193, 199, 211, 223, 283, 331, 349, 373, 379, 409, 421, 433, 463, 499, 541, 571, 601, 613, 619, 643, 709, 739, 769, 823, 829, 883, 991, 1009, 1021, 1039, 1051, 1063, 1129, 1213, 1231, 1291, 1303, 1423, 1453, 1471, 1549

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 10 2009

			2*3+11=17, which is prime.

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

Cf. A000040, A005382, A005384, A023204 - A023207, A063908 - A063912.

[p: p in PrimesUpTo(1600) | IsPrime(2*p+11)]; // Vincenzo Librandi, Apr 27 2014

Select[Prime[Range[6! ]],PrimeQ[2*#+11]&]

A023245 Primes that remain prime through 2 iterations of the function f(x) = 2x + 9.

Original entry on oeis.org

5, 11, 19, 31, 59, 61, 71, 101, 109, 151, 179, 239, 241, 269, 281, 389, 409, 439, 449, 521, 571, 641, 659, 719, 829, 911, 971, 1051, 1061, 1181, 1201, 1229, 1319, 1361, 1439, 1579, 1669, 1699, 1741, 1831, 1949, 2269, 2341, 2371, 2521, 2549, 2579, 2609, 2671

Offset: 1

David W. Wilson

nonn

Primes p such that 2*p+9 and 4*n+27 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023207 and A155722.

[n: n in [0..100000] | IsPrime(n) and IsPrime(2*n+9) and IsPrime(4*n+27)] // Vincenzo Librandi, Aug 04 2010

Select[Prime[Range[500]],And@@PrimeQ[Rest[NestList[2#+9&,#,2]]]&]  (* Harvey P. Dale, Mar 23 2011 *)

isok(n) = isprime(n) && isprime(2*n+9) && isprime(4*n+27); \\ Michel Marcus, Sep 12 2016

A290839 a(n) = smallest prime p such that 2p + 2n - 1 is prime.

Original entry on oeis.org

2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 5, 3, 2, 2, 7, 3, 2, 3, 2, 2, 3, 2, 7, 3, 2, 5, 3, 2, 2, 7, 3, 2, 3, 2, 2, 13, 3, 2, 3, 2, 11, 3, 2, 5, 7, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 13, 7, 11, 5, 19, 3, 2, 3, 2, 5, 3, 2, 2, 7, 5, 5, 3, 2, 2, 7, 3, 2, 13, 3, 2, 3, 2, 7, 3, 2

Offset: 0

XU Pingya, Aug 12 2017

Iain Fox, Table of n, a(n) for n = 0..20000

Cf. A005384, A023204, A023205, A023206, A023207, A171517, A020483, A290838.

Cf. A067076 (indices n at which a(n) = 2).

Table[j=0; found=False; While[!found, j++; found=PrimeQ[2Prime[j]+2n-1]]; Prime[j], {n, 85}]

a(n) = {my(p=2); while(!isprime(2*p+2*n-1), p = nextprime(p+1)); p;} \\ Michel Marcus, Aug 12 2017

a(-n) = A290838(n+1). - Iain Fox, Dec 14 2017

a(0) prepended by Iain Fox, Dec 14 2017

A023276 Primes that remain prime through 3 iterations of function f(x) = 2x + 9.

Original entry on oeis.org

5, 11, 31, 71, 281, 521, 911, 1181, 2371, 2521, 3391, 3701, 4211, 4931, 5051, 7211, 7411, 8221, 8431, 8461, 8501, 8641, 8951, 9601, 9871, 10301, 11981, 12421, 13121, 13921, 14591, 16381, 16451, 16901, 16931, 17791, 17881, 19391, 19751, 21991, 23021

Offset: 1

David W. Wilson

nonn

Primes p such that 2*p+9, 4*p+27 and 8*p+63 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023207, A023245, and of A155722.

[n: n in [1..100000] | IsPrime(n) and IsPrime(2*n+9) and IsPrime(4*n+27) and IsPrime(8*n+63)] // Vincenzo Librandi, Aug 04 2010

A023276:=n->`if`(isprime(n) and isprime(2*n+9) and isprime(4*n+27) and isprime(8*n+63), n, NULL): seq(A023276(n), n=1..10^5); # Wesley Ivan Hurt, Feb 11 2017

Select[Prime@ Range@ 2600, Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 9 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 19 2016 *)
Select[Prime[Range[3000]],AllTrue[Rest[NestList[2#+9&,#,3]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 01 2017 *)

is(n)=isprime(n) && isprime(2*n+9) && isprime(4*n+27) && isprime(8*n+63) \\ Charles R Greathouse IV, Sep 20 2016

a(n) == 1 (mod 10) for n > 1. - John Cerkan, Sep 16 2016

A153145 Primes p such that 2*p + 19 is also prime.

Original entry on oeis.org

2, 5, 11, 17, 41, 47, 59, 89, 107, 131, 137, 149, 167, 191, 251, 269, 311, 317, 389, 401, 419, 431, 461, 467, 479, 521, 587, 599, 641, 677, 797, 809, 839, 857, 929, 941, 947, 977, 1031, 1061, 1097, 1109, 1181, 1187, 1229, 1301, 1307, 1319, 1361, 1367, 1409

Offset: 1

Vincenzo Librandi, Dec 19 2008

			For n=2, 2*n+19 = 23 is prime, so 2 is in the sequence.

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

Cf. A153143 (m and 2*m+19 are both prime), A005384 (Sophie Germain primes, m and 2*m+1 are both prime), A023204 (m and 2*m+3 are both prime), A023205 (m and 2*m+5 are both prime), A023206 (m and 2*m+7 are both prime), A023207 (m and 2*m+9 are both prime).

[p: p in PrimesUpTo(1500) | IsPrime(2*p+19)];

Select[Prime[Range[2000]],PrimeQ[2 # + 19] &] (* Vincenzo Librandi, Oct 20 2012 *)

Edited, corrected and extended by Klaus Brockhaus, Dec 22 2008

A171518 Primes p such that 3*p-+8 are primes.

Original entry on oeis.org

5, 7, 13, 17, 53, 73, 83, 113, 127, 157, 193, 223, 277, 347, 367, 433, 613, 647, 673, 743, 797, 907, 937, 1117, 1217, 1373, 1427, 1483, 1543, 1597, 1637, 1667, 1877, 1933, 2027, 2237, 2297, 2447, 2647, 2687, 2843, 3083, 3137, 3613, 3797, 4073, 4463, 4483

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 10 2009

nonn

			5 is in the sequence since 3*5-8=7 and 3*5+8=23 are primes.

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Cf. A000040, A005382, A005384, A023204-A023207, A063908-A063912, A103803, A124098, A125272, A171517

Select[Prime[Range[7! ]],PrimeQ[3*#-8]&&PrimeQ[3*#+8]&]
Select[Prime[Range[700]],AllTrue[3#+{8,-8},PrimeQ]&] (* Harvey P. Dale, Feb 10 2025 *)

A190354 Primes p such that p,q,r,s are consecutive primes and 2p+9, 2q+9, 2r+9, 2s+9 are also primes.

Original entry on oeis.org

887, 907, 4211, 6569, 8447, 23339, 23357, 30809, 33427, 33937, 38839, 57529, 57557, 57859, 70271, 77621, 77641, 77647, 77659, 80747, 86587, 87691, 109537, 115769, 116041, 117251, 160681, 192781, 207797, 217387, 228257, 228281, 232457, 244339

Offset: 1

Pierre CAMI, May 09 2011

nonn

The smallest in a group of four consecutive primes in A023207. - R. J. Mathar, Jun 02 2011

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

isA023207 := proc(n) isprime(n) and isprime(2*n+9) ; end proc:
isA190354 := proc(n) local q,r,s ; if isprime(n) then q := nextprime(n) ; r := nextprime(q) ; s := nextprime(r) ; isA023207(n) and isA023207(q) and isA023207(r) and isA023207(s) ; else return false; end if; end proc:
for i from 1 do p := ithprime(i) ; if isA190354(p) then print(p) ; end if; end do: # R. J. Mathar, Jun 02 2011

p2Q[n_]:=And@@PrimeQ[2#+9&/@n]; Transpose[Select[Partition[Prime[ Range[22000]],4,1],p2Q]][[1]] (* Harvey P. Dale, Jun 10 2011 *)

old(p,k)=while(k--,p=precprime(p-1));p; k=0;forprime(p=2, 1e6,if(isprime(p+p+9),if(k++>3,print1(old(p,4)", ")),k=0))

cp's OEIS Frontend

A171517 Primes p such that 2*p+11 is prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

A023245 Primes that remain prime through 2 iterations of the function f(x) = 2x + 9.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A290839 a(n) = smallest prime p such that 2p + 2n - 1 is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A023276 Primes that remain prime through 3 iterations of function f(x) = 2x + 9.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A153145 Primes p such that 2*p + 19 is also prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Extensions

A171518 Primes p such that 3*p-+8 are primes.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A190354 Primes p such that p,q,r,s are consecutive primes and 2p+9, 2q+9, 2r+9, 2s+9 are also primes.

Views

Author

Keywords

Comments

Links

Programs

Maple

Mathematica

PARI