A089531 -id:A089531 - cp's OEIS frontend

A089532 A089531 indexed by A000040.

4, 6, 7, 10, 12, 13, 18, 24, 25, 29, 33, 35, 42, 45, 50, 55, 59, 60, 66, 68, 70, 77, 78, 79, 87, 88, 89, 100, 102, 104, 113, 123, 126, 127, 135, 136, 139, 142, 152, 158, 159, 165, 169, 172, 176, 184, 187, 189, 197, 199, 201, 203, 209, 211, 216, 234, 237, 244, 251

Offset: 1

Ray Chandler, Nov 07 2003

nonn

Cf. A023204, A089530, A089531.

a(n)=k such that A089531(n)=A000040(k).

A023204 Primes p such that 2*p + 3 is also prime.

Original entry on oeis.org

2, 5, 7, 13, 17, 19, 29, 43, 47, 53, 67, 73, 89, 97, 113, 127, 137, 139, 157, 167, 173, 193, 197, 199, 223, 227, 229, 269, 277, 283, 307, 337, 349, 353, 379, 383, 397, 409, 439, 463, 467, 487, 503, 509, 523, 547, 557, 563, 599, 607, 613, 617, 643, 647, 659, 739, 743, 773

Offset: 1

David W. Wilson

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

Cf. A089530, A089531, A089532.

[p: p in PrimesUpTo(1000) | IsPrime(2*p+3)]; // Vincenzo Librandi, Nov 20 2010

A023204 := proc (n) if isprime(n) and isprime(2*n+3) = true then n end if end proc; seq(A023204(n), n=1..1000); # Wesley Ivan Hurt, Jun 28 2014

f[n_]:=PrimeQ[2*n+3]; lst={};Do[p=Prime[n];If[f[p],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 03 2009 *)
Select[Prime[Range[200]],PrimeQ[2#+3]&] (* Harvey P. Dale, May 03 2012 *)

is(n)=isprime(2*n+3)&&isprime(n) \\ Charles R Greathouse IV, Jul 02 2013

A067076 INTERSECT A000040. - R. J. Mathar, Mar 23 2017

A092109 Primes p such that p+3 is a semiprime.

Original entry on oeis.org

3, 7, 11, 19, 23, 31, 43, 59, 71, 79, 83, 103, 131, 139, 163, 191, 199, 211, 223, 251, 271, 311, 331, 359, 379, 383, 419, 443, 463, 479, 499, 523, 563, 619, 631, 659, 691, 743, 839, 859, 863, 883, 911, 919, 971, 1039, 1091, 1123, 1151, 1171, 1223, 1231, 1259

Offset: 1

Zak Seidov, Feb 21 2004

Primes p such that p-3 is semiprime are in A089531; p and 2p+3 both prime, A023204; p, 2p-3 and 2p+3 prime, A092110.
Primes p such that (p+3)/2 is prime. All these primes are congruent to 3 mod 4. - Artur Jasinski, Oct 11 2008
Subsequence of A131426. - Zak Seidov, Mar 29 2015
Subsequence of A091305. - David Radcliffe, May 22 2022

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

Cf. A023204, A089531, A063908, A092110, A115334, A131426.

IsSemiprime:=func< p | &+[ k[2]: k in Factorization(p)] eq 2 >; [p: p in PrimesUpTo(1300)| IsSemiprime(p+3)]; // Vincenzo Librandi, Feb 21 2014

select(p -> isprime(p) and isprime((p+3)/2), [seq(2*k+1,k=1..1000)]); # Robert Israel, Mar 29 2015

aa = {}; k = 3; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 100}]; aa (* Artur Jasinski, Oct 11 2008 *)
Select[Prime[Range[300]],PrimeOmega[#+3]==2&] (* Harvey P. Dale, Feb 07 2018 *)

is(n)=n%2 && isprime((n+3)/2) && isprime(n) \\ Charles R Greathouse IV, Jul 12 2016

a(n) = 2*A063908(n)-3 = 4*A115334(n)+3. - Artur Jasinski, Oct 11 2008

A089530 A023204 indexed by A000040.

Original entry on oeis.org

1, 3, 4, 6, 7, 8, 10, 14, 15, 16, 19, 21, 24, 25, 30, 31, 33, 34, 37, 39, 40, 44, 45, 46, 48, 49, 50, 57, 59, 61, 63, 68, 70, 71, 75, 76, 78, 80, 85, 90, 91, 93, 96, 97, 99, 101, 102, 103, 109, 111, 112, 113, 117, 118, 120, 131, 132, 137, 139, 140, 144, 147, 149, 154

Offset: 1

Ray Chandler, Nov 07 2003

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

Cf. A023204, A089531, A089532.

[n: n in [1..250] | IsPrime(2*NthPrime(n)+3)]; // Vincenzo Librandi, May 02 2016

Select[Range[160], PrimeQ[2 Prime[#] + 3] &] (* Vincenzo Librandi, May 02 2016 *)

a(n)=k such that A023204(n)=A000040(k).

A092110 Primes p such that 2p+3 and 2p-3 are both prime.

Original entry on oeis.org

5, 7, 13, 17, 43, 53, 67, 97, 113, 127, 137, 157, 167, 193, 223, 283, 487, 547, 563, 613, 617, 643, 647, 743, 773, 937, 1033, 1187, 1193, 1277, 1427, 1453, 1483, 1543, 1583, 1627, 1663, 1733, 1847, 2027, 2143, 2297, 2393, 2437, 2467, 2477, 2503, 2617, 2843

Offset: 1

Zak Seidov, Feb 21 2004

Intersection of A023204 and A063908.

All numbers in this sequence end with 3 or 7 (except the first one, which is 5). See A136191 or A136192. - Carlos Alves, Dec 20 2007

			From _K. D. Bajpai_, Sep 08 2020: (Start)
7 is a term because 2*7 + 3 = 17 and 2*7 - 3 = 11 are both prime.
13 is a term because 2*13 + 3 = 29 and 2*13 - 3 = 23 are both prime.
(End)

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A023204, A089531, A063908, A092109.

Cf. A136191, A136192.

[p: p in PrimesUpTo(10000)|IsPrime(2*p-3) and IsPrime(2*p+3)] // Vincenzo Librandi, Nov 16 2010

select(p -> isprime(p) and isprime(2*p+3) and isprime(2*p-3), [seq(2*k+1, k=1..1000)]); # K. D. Bajpai, Sep 08 2020

Select[Prime@Range@1000,PrimeQ[2#-3]&&PrimeQ[2#+3]&] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2011 *)

A089528 Primes p of the form 2prime(k) + 3 such that 2prime(k+1) + 3 is the next prime after p.

Original entry on oeis.org

13, 37, 89, 277, 389, 397, 449, 457, 701, 761, 929, 2069, 2221, 2609, 2857, 3121, 3217, 3221, 6329, 7229, 7537, 7649, 8581, 8677, 9277, 9941, 11317, 11681, 12401, 13421, 13469, 15649, 16729, 17401, 17497, 17729, 18257, 19289, 19489, 19937, 20509

Offset: 1

Ray Chandler, Nov 07 2003

nonn

			p(3)=5, 2*5 + 3 = 13 = p(6);
p(4)=7, 2*7 + 3 = 17 = p(7).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Subsequence of A089531.

Cf. A089526, A089527, A089529.

Select[Partition[2#+3&/@Prime[Range[2500]],2,1],AllTrue[#,PrimeQ] && NextPrime[ #[[1]]]==#[[2]]&][[All,1]] (* Harvey P. Dale, Dec 14 2021 *)

forprime(p=2,10500,my(p23=2*p+3);if(isprime(p23),my(pp=2*nextprime(p+1)+3);if(isprime(pp)&&pp==nextprime(p23+1),print1(p23,", ")))) \\ Hugo Pfoertner, Aug 04 2021

a(n) = 2*A089527(n) + 3 = 2*A000040(A089526(n)) + 3 = A000040(A089529(n)).

Offset changed to 1 by Jinyuan Wang, Aug 04 2021

A230225 Primes p such that 2p+1 and 2p+3 are not prime.

Original entry on oeis.org

31, 37, 59, 61, 71, 79, 101, 103, 107, 109, 149, 151, 163, 181, 211, 241, 257, 263, 271, 311, 313, 317, 331, 347, 367, 373, 389, 401, 421, 433, 449, 457, 461, 479, 499, 521, 541, 569, 571, 577, 587, 601, 619, 631, 661, 673, 677, 691, 701, 709, 727, 733, 751

Offset: 1

Vincenzo Librandi, Oct 12 2013

			31 is in the sequence because 2*31+1=63 and 2*31+3=65 are not prime.

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

Cf. A005384, A023204, A053176, A089531, A126107, A163769, A230039, A230117.

[p: p in PrimesUpTo(2500)|not IsPrime(2*p+1) and not IsPrime(2*p+3)];

Select[Range[10^3], PrimeQ[#]&&!PrimeQ[2 # + 1]&&!PrimeQ[2 # + 3]&]
Select[Prime[Range[200]],NoneTrue[2#+{1,3},PrimeQ]&] (* Harvey P. Dale, Sep 19 2021 *)

A165947 Primes of the form 2q + 3 where q is composite.

Original entry on oeis.org

11, 19, 23, 31, 43, 47, 53, 59, 67, 71, 73, 79, 83, 101, 103, 107, 113, 127, 131, 139, 151, 157, 163, 167, 173, 179, 191, 193, 199, 211, 223, 227, 233, 239, 241, 251, 263, 269, 271, 283, 293, 307, 311, 313, 331, 347, 353, 359, 367, 373, 379, 383, 409, 419, 421

Offset: 1

Claudio Meller, Oct 01 2009

G. C. Greubel, Table of n, a(n) for n = 1..2500

Cf. A002808, A129069.

Select[Table[If[PrimeQ[n],0,2n+3],{n,2,500}],PrimeQ]  (* Harvey P. Dale, Mar 25 2011 *)

lista(nn) = forcomposite(q=4, nn, if(isprime(p=2*q+3), print1(p, ", "))); \\ Altug Alkan, Apr 18 2016

A000040 \ { {2,3,5} U A089531}. - R. J. Mathar, Oct 28 2009

A217197 Primes p such that p-3 is the greatest semiprime less than p.

Original entry on oeis.org

13, 29, 61, 109, 137, 149, 181, 197, 229, 257, 277, 281, 317, 349, 389, 401, 457, 461, 541, 557, 569, 617, 677, 761, 797, 821, 929, 937, 977, 1021, 1097, 1129, 1217, 1237, 1289, 1297, 1321, 1481, 1489, 1549, 1597, 1621, 1721, 1777, 1861, 1877, 1997, 2029

Offset: 1

Antonio Roldán, Sep 27 2012

nonn

Subsequence of A089531.

			977 is prime, 976 = 2^4*61 and 975 = 3*5^2*13 are not semiprimes, 974 = 2*487 is a semiprime.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A217195.

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Prime[Range[500]], ! SemiPrimeQ[# - 1] && ! SemiPrimeQ[# - 2] && SemiPrimeQ[# - 3] &] (* T. D. Noe, Sep 27 2012 *)

forprime(p=5, 9999, bigomega(p-3)==2 && bigomega(p-1)!=2 && bigomega(p-2)!=2 & print1(p", "))

A247010 Primes p such that (p-3)/2 and 2*p+3 are both prime.

Original entry on oeis.org

7, 13, 17, 29, 89, 97, 137, 197, 229, 277, 337, 349, 397, 557, 617, 797, 929, 937, 1117, 1217, 1237, 1777, 2129, 2309, 2437, 2477, 2617, 2749, 2857, 2909, 3049, 3109, 3137, 3329, 3389, 4057, 4229, 4289, 4409, 5237, 5297, 5417, 5557, 5717, 5857, 6689

Offset: 1

Vincenzo Librandi, Sep 09 2014

A023204 INTERSECT A089531. After 7, all terms are obviously in A002144.

Conjecture: the sequence is infinite.

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

Cf. A023204, A023242, A089531.

[p: p in PrimesUpTo(7000) | IsPrime((p-3)div 2) and IsPrime(2*p+3)];

Select[Prime[Range[900]], And@@PrimeQ/@{(# - 3)/2, 2 # + 3} &]

is(n)=isprime(n) && isprime(2*n+3) && isprime((n-3)\2) \\ Charles R Greathouse IV, Sep 09 2014

def t(i): return 2*i+3
[t(p) for p in primes(5000) if is_prime(t(p)) and is_prime(t(t(p)))] # Bruno Berselli, Sep 09 2014

a(n) = 2*A023242(n) + 3. [Bruno Berselli, Sep 09 2014]

cp's OEIS Frontend

A089532 A089531 indexed by A000040.

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A023204 Primes p such that 2*p + 3 is also prime.

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A092109 Primes p such that p+3 is a semiprime.

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A089530 A023204 indexed by A000040.

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A092110 Primes p such that 2p+3 and 2p-3 are both prime.

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A089528 Primes p of the form 2*prime(k) + 3 such that 2*prime(k+1) + 3 is the next prime after p.

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A230225 Primes p such that 2*p+1 and 2*p+3 are not prime.

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A165947 Primes of the form 2q + 3 where q is composite.

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A089528 Primes p of the form 2prime(k) + 3 such that 2prime(k+1) + 3 is the next prime after p.

A230225 Primes p such that 2p+1 and 2p+3 are not prime.