A089530 -id:A089530 - cp's OEIS frontend

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

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

A089531 Primes p such that (p-3)/2 is also prime.

Original entry on oeis.org

7, 13, 17, 29, 37, 41, 61, 89, 97, 109, 137, 149, 181, 197, 229, 257, 277, 281, 317, 337, 349, 389, 397, 401, 449, 457, 461, 541, 557, 569, 617, 677, 701, 709, 761, 769, 797, 821, 881, 929, 937, 977, 1009, 1021, 1049, 1097, 1117, 1129, 1201, 1217, 1229, 1237

Offset: 1

Ray Chandler, Nov 07 2003

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

Cf. A023204, A089530, A089532.

[p: p in PrimesUpTo(1300) | IsPrime((p-3) div 2)]; // Vincenzo Librandi, Apr 13 2013

Clear[lst,n,f] f[n_]:=PrimeQ[(n-3)/2]; lst={};Do[p=Prime[n];If[f[p],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 13 2009 *)
Select[Prime[Range[300]], PrimeQ[(# - 3) / 2]&] (* Vincenzo Librandi, Apr 13 2013 *)

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

a(n) = 2*A023204(n) + 3.

Comment from Juri-Stepan Gerasimov used as new name (old name moved to formulas). - Charles R Greathouse IV, Sep 09 2014

A089526 Numbers n such that 2p(n)+3 and 2p(n+1)+3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

3, 7, 14, 33, 44, 45, 48, 49, 70, 75, 90, 174, 186, 213, 225, 246, 253, 254, 447, 505, 524, 531, 589, 592, 625, 665, 745, 766, 806, 866, 868, 989, 1047, 1084, 1091, 1105, 1131, 1191, 1202, 1228, 1257, 1280, 1333, 1395, 1410, 1429, 1495, 1512, 1550, 1643, 1651

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 A089530. Cf. A089527, A089528, A089529.

cpQ[n_]:=Module[{p=2Prime[n]+3},PrimeQ[p]&&NextPrime[p]==2Prime[n+1]+3]; Select[Range[1700],cpQ] (* Harvey P. Dale, Nov 29 2014 *)

A089532 A089531 indexed by A000040.

Original entry on oeis.org

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).

A190478 a(n) is the smallest prime prime(k) > a(n-1) such that the n numbers 2*prime(j)+3, j=k to k+n-1, are all prime.

Original entry on oeis.org

2, 5, 13, 3767, 19913, 726109, 4827859, 59069473, 179993463679, 2280987436223

Offset: 1

Pierre CAMI, May 11 2011

This essentially searches for blocks of n consecutive primes of the form A023204 (see also A089530) with a minimum of the primes in the block set by the previous entry in the sequence. - R. J. Mathar, Jun 02 2011

Any further terms are > 10^13. - Lucas A. Brown, Mar 17 2024

			For n=1, 2 is prime and 2*2+3=7 is prime so a(1)=2.
For n=2, 5,7 are consecutive primes 2*5+3 and 2*7+3 are primes so a(2)=5 as 5 is the least such prime > 2.
For n=3, 13,17,19 are consecutive primes 2*13+3, 2*17+3, 2*19+3 are primes so a(3)=13 as 13 is the least such prime > 5.

Lucas A. Brown, Python program.

Cf. A023204.

isA023204 := proc(n) isprime(n) and isprime(2*n+3) ; end proc:
A190478idx := proc(n) option remember; if n = 1 then 1; else for a from procname(n-1)+1 do krun := true; for k from a to a+n-1 do if not isA023204(ithprime(k)) then krun := false; break; end if; end do: if krun then return a; end if; end do: end if; end proc:
A190478 := proc(n) ithprime( A190478idx(n)) ; end proc: # R. J. Mathar, Jun 02 2011

old(p,k)=while(k--,p=precprime(p-1));p;
n=1;k=0;forprime(p=2,4e9,if(isprime(p<<1+3),if(k++==n,print1(old(p,n)", ");k--;n++),k=0)) \\ Charles R Greathouse IV, May 11 2011

a(8) from Charles R Greathouse IV, May 11 2011

a(9)-a(10) from Lucas A. Brown, Mar 17 2024

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

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A089531 Primes p such that (p-3)/2 is also prime.

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A089526 Numbers n such that 2*p(n)+3 and 2*p(n+1)+3 are consecutive primes, where p(i) denotes the i-th prime.

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A089532 A089531 indexed by A000040.

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A190478 a(n) is the smallest prime prime(k) > a(n-1) such that the n numbers 2*prime(j)+3, j=k to k+n-1, are all prime.

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A089526 Numbers n such that 2p(n)+3 and 2p(n+1)+3 are consecutive primes, where p(i) denotes the i-th prime.