A023206 -id:A023206 - cp's OEIS frontend

A023244 Primes that remain prime through 2 iterations of the function f(x) = 2x + 7.

2, 5, 17, 23, 53, 83, 137, 197, 227, 257, 293, 317, 347, 383, 467, 593, 647, 677, 683, 797, 857, 953, 1163, 1193, 1217, 1607, 1877, 1907, 1913, 1997, 2063, 2207, 2237, 2843, 2903, 3023, 3257, 3323, 3557, 3947, 4133, 4253, 4517, 4583, 4643, 4967, 5087, 5387

Offset: 1

David W. Wilson

nonn

Primes p such that 2*p+7 and 4*p+21 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023206 and A105760.

[n: n in [0..100000] | IsPrime(n) and IsPrime(2*n+7) and IsPrime(4*n+21)] // Vincenzo Librandi, Aug 04 2010

Select[Prime@ Range[10^3], Times @@ Boole@ PrimeQ@ NestList[2 # + 7 &, #, 2] > 0 &] (* Michael De Vlieger, Sep 12 2016 *)

a(n) == 5 (mod 6), for n > 1. - John Cerkan, Sep 12 2016

A023275 Primes that remain prime through 3 iterations of function f(x) = 2x + 7.

Original entry on oeis.org

5, 23, 293, 593, 953, 2063, 3323, 4133, 4583, 8243, 8783, 9173, 9203, 14723, 15383, 16103, 16763, 18413, 19163, 20123, 25733, 29453, 37223, 38783, 39443, 40253, 41903, 42923, 44753, 45863, 49433, 51473, 54443, 54623, 54713, 57383, 58913, 63353, 66533

Offset: 1

David W. Wilson

nonn

Primes p such that 2*p+7, 4*p+21 and 8*p+49 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023206, A023244, and of A105760.

[n: n in [1..100000] | IsPrime(n) and IsPrime(2*n+7) and IsPrime(4*n+21) and IsPrime(8*n+49)] // Vincenzo Librandi, Aug 04 2010

Select[Prime@ Range@ 7000, Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 7 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 19 2016 *)
Select[Prime[Range[7000]],AllTrue[Rest[NestList[2#+7&,#,3]],PrimeQ]&] (* Harvey P. Dale, Dec 26 2022 *)

is(n)=isprime(n) && isprime(2*n+7) && isprime(4*n+21) && isprime(8*n+49) \\ Charles R Greathouse IV, Sep 20 2016

a(n) == 23 (mod 30) for n > 1. - John Cerkan, Sep 16 2016

A023305 Primes that remain prime through 4 iterations of function f(x) = 2x + 7.

Original entry on oeis.org

293, 2063, 4583, 9203, 14723, 20123, 25733, 29453, 40253, 54713, 76103, 97523, 99833, 109433, 138683, 149993, 158243, 196853, 199403, 218873, 253103, 297623, 379913, 416963, 445463, 468113, 508073, 551963, 562403, 564713, 574703, 583733

Offset: 1

David W. Wilson

nonn

Primes p such that 2*p+7, 4*p+21, 8*p+49 and 16*p+105 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023206, A023244, A023275, and A105760.

[n: n in [1..1000000] | IsPrime(n) and IsPrime(2*n+7) and IsPrime(4*n+21) and IsPrime(8*n+49) and IsPrime(16*n+105)] // Vincenzo Librandi, Aug 04 2010

rp4Q[n_]:=AllTrue[Rest[NestList[2#+7&,n,4]],PrimeQ]; Select[Prime[Range[ 50000]],rp4Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 30 2020 *)

a(n) == 3 (mod 10). - John Cerkan, Oct 04 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

A023333 Primes that remain prime through 5 iterations of function f(x) = 2x + 7.

Original entry on oeis.org

14723, 20123, 54713, 109433, 594653, 604883, 676493, 759953, 847103, 935843, 1035743, 1049603, 1079033, 1099823, 1222253, 1263323, 1499153, 1754033, 1835003, 1893173, 2017283, 2071493, 2099213, 2199653, 2895743, 2998313, 3389693, 4133663

Offset: 1

David W. Wilson

nonn

Primes p such that 2*p+7, 4*p+21, 8*p+49, 16*p+105 and 32*p+217 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023206, A023244, A023275, A023305, and A105760.

[n: n in [1..5000000] | IsPrime(n) and IsPrime(2*n+7) and IsPrime(4*n+21) and IsPrime(8*n+49) and IsPrime(16*n+105) and IsPrime(32*n+217)] // Vincenzo Librandi, Aug 04 2010

a(n) == 23 (mod 30). - John Cerkan, Oct 10 2016

A106086 Primes p such that 7p + 2 and 2p + 7 are primes.

Original entry on oeis.org

3, 5, 11, 23, 47, 53, 71, 131, 173, 197, 251, 257, 293, 317, 383, 461, 467, 587, 593, 683, 701, 773, 797, 863, 953, 983, 1031, 1103, 1151, 1187, 1193, 1217, 1301, 1307, 1373, 1451, 1481, 1607, 1721, 1787, 2111, 2207, 2237, 2333, 2633, 2903, 3023, 3221, 3347

Offset: 1

Zak Seidov, May 07 2005

nonn

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

Cf. A105760 (2n+7 is prime), A105772 (7n+2 is prime).

Cf. A107438, A023206.

[p: p in PrimesUpTo(5000)|IsPrime(7*p+2) and IsPrime(2*p+7)] // Vincenzo Librandi, Jan 30 2011

Select[Prime[Range[220]], PrimeQ[2#+7]&&PrimeQ[7#+2]&]

More terms from Rick L. Shepherd, Jan 29 2006

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

A166009 Primes of the form 7 + 2*p, where p is a prime.

Original entry on oeis.org

11, 13, 17, 29, 41, 53, 89, 101, 113, 149, 173, 233, 269, 281, 353, 389, 401, 461, 509, 521, 569, 593, 641, 701, 773, 809, 929, 941, 1013, 1049, 1181, 1193, 1289, 1301, 1361, 1373, 1409, 1493, 1553, 1601, 1721, 1733, 1889, 1901, 1913, 1949, 1973, 2069, 2129

Offset: 1

Vincenzo Librandi, Oct 04 2009

nonn

Starting with n=3 both a(n) and A023206(n) == 5 mod 6. - Zak Seidov, Oct 23 2009

			13 is in the sequence because 13 = 7 + 2*3 and 3 are both primes.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A023206. - Zak Seidov, Oct 23 2009

Clear[lst,n,f] f[n_]:=PrimeQ[(n-1)/2-3]; lst={};Do[p=Prime[n];If[f[p],AppendTo[lst,p]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 13 2009 *)
s={11,13};Do[If[PrimeQ[n]&&PrimeQ[(n-7)/2],AppendTo[s,n]],{n,17,10^3,6}];s (* Zak Seidov, Oct 23 2009 *)
Select[2#+7&/@Prime[Range[200]],PrimeQ] (* Harvey P. Dale, Dec 15 2010 *)

lista(nn) = {forprime(p=2, nn, if (isprime(q=2*p+7), print1(q, ", ")););} \\ Michel Marcus, Nov 08 2014

a(n) = 7 + 2*A023206(n). - R. J. Mathar, Oct 05 2009

1089 replaced with 1049 by R. J. Mathar, Oct 05 2009

cp's OEIS Frontend

A023244 Primes that remain prime through 2 iterations of the function f(x) = 2x + 7.

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A023275 Primes that remain prime through 3 iterations of function f(x) = 2x + 7.

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A023305 Primes that remain prime through 4 iterations of function f(x) = 2x + 7.

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

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A023333 Primes that remain prime through 5 iterations of function f(x) = 2x + 7.

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Magma

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A106086 Primes p such that 7*p + 2 and 2*p + 7 are primes.

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Magma

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

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Magma

Mathematica

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A166009 Primes of the form 7 + 2*p, where p is a prime.

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A106086 Primes p such that 7p + 2 and 2p + 7 are primes.