A023205 -id:A023205 - cp's OEIS frontend

A023206 Numbers m such that m and 2*m + 7 both prime.

2, 3, 5, 11, 17, 23, 41, 47, 53, 71, 83, 113, 131, 137, 173, 191, 197, 227, 251, 257, 281, 293, 317, 347, 383, 401, 461, 467, 503, 521, 587, 593, 641, 647, 677, 683, 701, 743, 773, 797, 857, 863, 941, 947, 953, 971, 983, 1031, 1061, 1103, 1151, 1163, 1187, 1193, 1217

Offset: 1

David W. Wilson

Subsequence of A105760. Except for the first two terms, all terms are congruent to 5 mod 6. - John Cerkan, Sep 07 2016

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

Cf. A005384, A023204, A023205.

[n: n in [0..1000] | IsPrime(n) and IsPrime(2*n+7)]; // Vincenzo Librandi, Nov 20 2010

A023206:=n->`if`(isprime(n) and isprime(2*n+7), n, NULL): seq(A023206(n), n=1..3*1000); # Wesley Ivan Hurt, Sep 07 2016

Select[Prime@Range@250,PrimeQ[2#+7]&] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2011 *)

is(n)=isprime(2*n+7) && isprime(n) \\ Charles R Greathouse IV, Sep 07 2016

A023207 Numbers m such that m and 2*m + 9 both prime.

Original entry on oeis.org

2, 5, 7, 11, 17, 19, 29, 31, 37, 47, 59, 61, 71, 79, 101, 107, 109, 127, 131, 137, 149, 151, 179, 211, 227, 229, 239, 241, 257, 269, 277, 281, 311, 317, 337, 359, 367, 389, 401, 409, 439, 449, 479, 487, 491, 521, 541, 547, 557, 571, 577, 607, 641, 647, 659, 709, 719, 739

Offset: 1

David W. Wilson

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

Cf. A005384, A023204, A023205.

[ n: n in PrimesUpTo(1000) | IsPrime(2*n+9) ]; // Vincenzo Librandi, Nov 20 2010

Select[Prime@Range@250,PrimeQ[2#+9]&] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2011 *)

A023243 Primes that remain prime through 2 iterations of the function f(x) = 2x + 5.

Original entry on oeis.org

7, 13, 31, 37, 67, 73, 79, 139, 151, 181, 367, 541, 613, 661, 709, 739, 787, 811, 829, 997, 1087, 1117, 1123, 1249, 1327, 1669, 1753, 1801, 1861, 1999, 2011, 2113, 2179, 2239, 2293, 2473, 2557, 2659, 2713, 2719, 3037, 3181, 3187, 3271, 3301, 3517, 3727, 3793

Offset: 1

David W. Wilson

Primes p such that 2*p+5 and 4*p+15 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023205 and A089038.

[n: n in [0..100000] | IsPrime(n) and IsPrime(2*n+5) and IsPrime(4*n+15)] // Vincenzo Librandi, Aug 04 2010

is(n)=n%6==1 && isprime(2*n+5) && isprime(4*n+15) && isprime(n) \\ Charles R Greathouse IV, Sep 12 2016

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

A023274 Primes that remain prime through 3 iterations of function f(x) = 2x + 5.

Original entry on oeis.org

13, 31, 37, 67, 73, 181, 367, 541, 661, 997, 1087, 1117, 1327, 1861, 2179, 2293, 2473, 2713, 2719, 3271, 3727, 4363, 5281, 5443, 5749, 7459, 8089, 8707, 9109, 9181, 9337, 10357, 10639, 12553, 13183, 14923, 16183, 16249, 17341, 17419, 17761, 17923, 17989

Offset: 1

David W. Wilson

nonn

Primes p such that 2*p+5, 4*p+15 and 8*p+35 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023205, A023243, and of A089038.

[n: n in [1..100000] | IsPrime(n) and IsPrime(2*n+5) and IsPrime(4*n+15) and IsPrime(8*n+35)] // Vincenzo Librandi, Aug 04 2010

select(t -> isprime(t) and isprime(2*t+5) and isprime(4*t+15) and isprime(8*t+35), [seq(t,t=7..20000,6)]);# Robert Israel, Sep 18 2016

Select[Prime@ Range@ 2100, Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 5 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 16 2016 *)

a(n) == 1 (mod 6). - John Cerkan, Sep 16 2016

A023304 Primes that remain prime through 4 iterations of function f(x) = 2x + 5.

Original entry on oeis.org

13, 31, 181, 541, 661, 1087, 1861, 2179, 2719, 3727, 7459, 8089, 8707, 9109, 10639, 17341, 19333, 22501, 23293, 29287, 32797, 39847, 40387, 42703, 46591, 51613, 53101, 56149, 56809, 57829, 59233, 80779, 87643, 89113, 89413, 91291, 93979, 94261, 98899

Offset: 1

David W. Wilson

nonn

Primes p such that 2*p+5, 4*p+15, 8*p+35 and 16*p+75 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023205, A023243, A023274, and A089038.

[n: n in [1..1000000] | IsPrime(n) and IsPrime(2*n+5) and IsPrime(4*n+15) and IsPrime(8*n+35) and IsPrime(16*n+75)]; // Vincenzo Librandi, Aug 04 2010

Select[Prime@ Range[10^4], Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 5 &, #, 4] > 0 &] (* Michael De Vlieger, Sep 27 2016 *)
Select[Prime[Range[10000]],AllTrue[Rest[NestList[2#+5&,#,4]],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 23 2020 *)

a(n) == 1 (mod 6). - John Cerkan, Sep 27 2016

Definition clarified by Harvey P. Dale, Oct 23 2020

A023332 Primes that remain prime through 5 iterations of function f(x) = 2x + 5.

Original entry on oeis.org

13, 541, 1087, 1861, 3727, 23293, 40387, 87643, 98899, 109111, 115153, 116329, 119101, 131617, 133597, 163909, 197521, 214021, 215389, 218227, 238207, 263239, 294751, 489901, 493693, 665527, 734131, 767881, 808693, 895351, 1038127, 1051957

Offset: 1

David W. Wilson

nonn

Primes p such that 2*p+5, 4*p+15, 8*p+35, 16*p+75 and 32*p+155 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023205, A023243, A023274, A023304, and A089038.

[n: n in [1..5000000] | IsPrime(n) and IsPrime(2*n+5) and IsPrime(4*n+15) and IsPrime(8*n+35) and IsPrime(16*n+75) and IsPrime(32*n+155)] // Vincenzo Librandi, Aug 04 2010

txQ[p_]:=AllTrue[NestList[2#+5&,p,5],PrimeQ]; Select[Prime[Range[83000]],txQ] (* Harvey P. Dale, May 10 2024 *)

a(n) == 1 (mod 6). - John Cerkan, Oct 09 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

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

cp's OEIS Frontend

A023206 Numbers m such that m and 2*m + 7 both prime.

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A023207 Numbers m such that m and 2*m + 9 both prime.

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A023243 Primes that remain prime through 2 iterations of the function f(x) = 2x + 5.

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A023274 Primes that remain prime through 3 iterations of function f(x) = 2x + 5.

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A023304 Primes that remain prime through 4 iterations of function f(x) = 2x + 5.

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A023332 Primes that remain prime through 5 iterations of function f(x) = 2x + 5.

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

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