A087695 -id:A087695 - cp's OEIS frontend

A087696 Numbers n such that n + 5 and n - 5 are both prime.

8, 12, 18, 24, 36, 42, 48, 66, 78, 84, 102, 108, 132, 144, 162, 168, 186, 228, 234, 246, 276, 288, 312, 342, 354, 378, 384, 414, 426, 438, 444, 462, 504, 552, 582, 612, 636, 648, 678, 696, 714, 738, 756, 792, 816, 834, 858, 882, 924, 942, 972

Offset: 1

Zak Seidov, Sep 27 2003

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A014574, A087678-A087683, A087695-A087697, A088765.

Select[Range[5,1000],AllTrue[#+{5,-5},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 08 2014 *)

isok(n) = isprime(n-5) && isprime(n+5); \\ Michel Marcus, Sep 02 2019

A087680 Numbers n such that n + 4 and n - 4 are both prime.

Original entry on oeis.org

7, 9, 15, 27, 33, 57, 63, 75, 93, 105, 135, 153, 177, 195, 237, 267, 273, 363, 393, 405, 435, 453, 483, 495, 567, 573, 597, 603, 657, 687, 705, 723, 747, 765, 825, 915, 933, 987, 1017, 1035, 1065, 1113, 1167, 1197, 1227, 1233, 1287, 1293, 1323, 1377, 1443

Offset: 1

Zak Seidov, Sep 27 2003

All terms > 7 (prime) are divisible by 3. Also note that n-4 and n+4 are not necessarily consecutive primes. First case when n-4 and n+4 are consecutive primes is for n=93 with n-4=89 and n+4=97. - Zak Seidov, Apr 22 2015

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A023202, A014574, A087678-A087683, A087695-A087697, A088764.

ZL:=[]:for p from 1 to 1444 do if (isprime(p) and isprime(p+8) ) then ZL:=[op(ZL),(p+(p+8))/2]; fi; od; print(ZL); # Zerinvary Lajos, Mar 07 2007

f[n_]:=PrimeQ[n-4]&&PrimeQ[n+4]; lst={};Do[If[f[n],AppendTo[lst,n]],{n,3,8!,2}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 09 2009 *)
Select[Prime[Range[250]],PrimeQ[#+8]&]+4 (* Harvey P. Dale, May 21 2023 *)

a(n) = A023202(n) + 4. - Michel Marcus, Apr 22 2015

More terms from Ray Chandler, Oct 26 2003

A087682 Numbers n such that n + 8 and n - 8 are both prime.

Original entry on oeis.org

11, 15, 21, 39, 45, 51, 75, 81, 105, 159, 165, 171, 189, 219, 231, 249, 285, 339, 345, 375, 381, 441, 471, 495, 549, 555, 579, 585, 609, 639, 651, 669, 735, 765, 819, 831, 945, 975, 1005, 1041, 1095, 1101, 1179, 1209, 1221, 1299, 1311, 1431, 1479, 1491

Offset: 1

Zak Seidov, Sep 27 2003

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A014574, A087678-A087683, A087695-A087697, A088768.

f[n_]:=PrimeQ[n-8]&&PrimeQ[n+8]; lst={};Do[If[f[n],AppendTo[lst,n]],{n,7,8!,2}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 09 2009 *)

More terms from Ray Chandler, Oct 26 2003

A104227 Primes one less than the sum over a sexy prime pair.

Original entry on oeis.org

19, 31, 67, 79, 127, 139, 151, 199, 211, 307, 547, 619, 739, 751, 919, 1087, 1231, 1459, 1471, 1759, 1987, 2131, 2179, 2239, 2251, 2467, 2647, 2851, 2971, 3319, 3331, 3391, 3499, 3511, 3559, 3571, 3727, 3739, 4027, 4567, 4759, 5107, 5347, 5419, 5431, 6367, 6607, 6619, 7027, 7219, 7459

Offset: 1

Giovanni Teofilatto, Apr 02 2005

Primes of the form A023201(i)+A046117(i)-1 or of the form 2*A087695(j)-1.

			19=7+13-1 is a prime and one less than the sum 7+13 over the second sexy prime pair.

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

Cf. A023201, A046117, A104228, A104229.

Select[2#+5&/@Select[Prime[Range[600]],PrimeQ[#+6]&],PrimeQ] (* Harvey P. Dale, Jan 04 2020 *)

Corrected definition. Extended beyond a(7). - R. J. Mathar, Nov 26 2008

A104010 Sum of two successive sexy primes.

Original entry on oeis.org

16, 20, 28, 32, 40, 52, 68, 80, 88, 100, 112, 128, 140, 152, 172, 200, 208, 212, 220, 268, 308, 320, 340, 352, 388, 392, 452, 460, 472, 508, 520, 532, 548, 560, 620, 628, 668, 700, 712, 740, 752, 772, 872, 892, 920, 928, 1012, 1088, 1120, 1132, 1148, 1180, 1192

Offset: 1

Giovanni Teofilatto, Mar 31 2005

Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- _N. J. A. Sloane_, Mar 07 2021].

Cf. A023201, A046117.

A104010 := proc(n)
    2*A023201(n)+6 ;
end proc: # R. J. Mathar, May 28 2013

a(n)= A023201(n)+A046117(n) = 2*A087695(n). [From R. J. Mathar, Nov 26 2008]

20 added, 84 removed, extended by R. J. Mathar, Nov 26 2008

A144842 Numbers k such that the three numbers k+3, k-3 and k+5 are all prime.

Original entry on oeis.org

8, 14, 26, 56, 104, 134, 176, 194, 236, 266, 566, 596, 656, 824, 1016, 1226, 1286, 1484, 1604, 1616, 1874, 2084, 2336, 2546, 2966, 3254, 3326, 3464, 3536, 3764, 3914, 3926, 4016, 4214, 4256, 4646, 4796, 5006, 5276, 5474, 5654, 5846, 5864, 6266, 6356, 6566

Offset: 1

Giovanni Teofilatto, Sep 22 2008

Subset of A087695. - R. J. Mathar, Sep 24 2008

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Triplet.

Cf. A046138, A087695, A086801, A144840.

Select[Range[7000], And @@ PrimeQ[# + {-3, 3, 5}] &] (* Amiram Eldar, Apr 14 2022 *)

from sympy import isprime
def ok(n): return n > 4 and isprime(n-3) and isprime(n+3) and isprime(n+5)
print(list(filter(ok, range(6567)))) # Michael S. Branicky, Aug 14 2021

a(n) = A046138(n) + 3. - R. J. Mathar, Sep 24 2008

Definition edited and extended by R. J. Mathar, Sep 24 2008

A164570 Primes p such that 8p-3 and 8p+3 are also prime numbers.

Original entry on oeis.org

2, 5, 7, 13, 47, 103, 107, 127, 163, 233, 293, 337, 383, 433, 443, 467, 503, 673, 677, 733, 797, 877, 1087, 1093, 1153, 1217, 1223, 1307, 1637, 1933, 2053, 2087, 2137, 2423, 2477, 2543, 2633, 2687, 2857, 2917, 3163, 3373, 3407, 3467, 3767, 3793, 3877

Offset: 1

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Subsequence of A023229. [R. J. Mathar, Aug 26 2009]

Primes of the form A087695(k)/8. [R. J. Mathar, Aug 26 2009]

			For p=2, 8*2-3=13 and 8*2+3=19 are prime numbers, which adds p=2 to the sequence
For p=5, 8*5-3=37 and 8*5+3=43 are prime numbers, which adds p=5 to the sequence.

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

Cf. A023212, A023217, A023224, A023230, A023239, A060212, A106015, A124098, A125272, A127430, A153768, A164566, A164567, A164568, A164569.

[p: p in PrimesUpTo(3000) | IsPrime(8*p-3) and IsPrime(8*p+3)]; // Vincenzo Librandi, Apr 09 2013

lst={};Do[p=Prime[n];If[PrimeQ[8*p-3]&&PrimeQ[8*p+3],AppendTo[lst,p]], {n,7!}];lst
Select[Prime[Range[1000]], And@@PrimeQ/@{8 # + 3, 8 # - 3}&] (* Vincenzo Librandi, Apr 09 2013 *)
Select[Prime[Range[1000]],AllTrue[8#+{3,-3},PrimeQ]&] (* Harvey P. Dale, May 05 2023 *)

Comments turned into examples by R. J. Mathar, Aug 26 2009

A179485 Sums of two successive primes s such that s+-3 are primes.

Original entry on oeis.org

8, 100, 1120, 1220, 1300, 2240, 2380, 2414, 3536, 3634, 4906, 4940, 5566, 5740, 6706, 7240, 8864, 9224, 9394, 10136, 10850, 12040, 12476, 12586, 12920, 13180, 13334, 13754, 14630, 14720, 15134, 16270, 17710, 18430, 18800, 19916, 21014, 21320

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 16 2010

nonn

Intersection of A001043 and A087695. - Robert Israel, Oct 25 2017

			3+5=8,8-3=5(prime),8+3=11(prime),..

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A074924, A074925, A167597, A176984, A176986, A075593, A075594, A116360, A076565

Cf. A001043, A087695.

q:= 2; p:= 3;
count:= 0:
while count < 100 do
  q:= p; p:= nextprime(p);
  s:= q+p;
  if isprime(s-3) and isprime(s+3) then
    count:= count+1; A[count]:= s;
  fi
od:
seq(A[i],i=1..count); # Robert Israel, Oct 25 2017

q=3;Select[Table[Prime[n]+Prime[n+1],{n,7!}],PrimeQ[ #-q]&&PrimeQ[ #+q]&]
Select[Total/@Partition[Prime[Range[1400]],2,1],AllTrue[#+{3,-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 04 2018 *)

A293271 Numbers n such that n - p and n + p are both prime for some prime p.

Original entry on oeis.org

5, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 30, 32, 34, 36, 39, 40, 42, 44, 45, 46, 48, 50, 54, 56, 60, 64, 66, 69, 70, 72, 76, 78, 81, 84, 86, 90, 92, 96, 99, 100, 102, 104, 105, 106, 108, 110, 111, 114, 116, 120, 126, 129, 130, 132, 134, 138, 140, 142

Offset: 1

Gionata Neri, Oct 04 2017

nonn

Apart from a(1), all terms are composite.

Union of A087679 and 2*A063713. - Robert Israel, Oct 09 2017

Cf. A087679, A087695, A087696, A087697 (subsequences).

Cf. A063713.

filter:= proc(n) local k;
  k:= 1;
  while k < n do
    k:= nextprime(k);
    if isprime(n+k) and isprime(n-k) then return true fi
  od;
  false
end proc:
select(filter, [$1..1000]); # Robert Israel, Oct 09 2017

Select[Range@ 142, Function[n, AnyTrue[Prime@ Range@ PrimePi@ n, PrimeQ[n + {-#, #}] == {True, True} &]]] (* Michael De Vlieger, Oct 09 2017 *)

a(n) = forprime(p=1, n, i=n-p; j=n+p; if(isprime(i)&&isprime(j), n; break))

cp's OEIS Frontend

A087696 Numbers n such that n + 5 and n - 5 are both prime.

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A087680 Numbers n such that n + 4 and n - 4 are both prime.

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A087682 Numbers n such that n + 8 and n - 8 are both prime.

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A104227 Primes one less than the sum over a sexy prime pair.

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A104010 Sum of two successive sexy primes.

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A144842 Numbers k such that the three numbers k+3, k-3 and k+5 are all prime.

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A164570 Primes p such that 8*p-3 and 8*p+3 are also prime numbers.

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Magma

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A179485 Sums of two successive primes s such that s+-3 are primes.

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A164570 Primes p such that 8p-3 and 8p+3 are also prime numbers.