A022004 -id:A022004 - cp's OEIS frontend

A372319 Products of prime triples (p, p+2, p+6) where p = A022004(n).

385, 2431, 7429, 82861, 1113121, 1317919, 7262011, 12112039, 30857731, 42749359, 99677881, 266669461, 558789841, 635308669, 690017701, 1308131911, 2095502089, 2215630321, 2922149239, 3265932301, 3305715499, 4170674419, 6577726891, 7995982009, 9046566901, 11234386249

Offset: 1

Michael De Vlieger, Jun 29 2024

Subsequence of A120944, subsequence of A007304.

Terms are congruent to 1 (mod 6), since A022004(n) is congruent to 5 mod 6, and 5+2 and 5+6 are congruent to 1 and 5 (mod 6), respectively. The product 5*1*5 is congruent to 1 (mod 6).

			a(1) = 385 = 5 * 7 * 11.
a(2) = 2431 = 11 * 13 * 17.
a(3) = 7429 = 17 * 19 * 23, etc.

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

Cf. A007304, A016921, A022004, A120944.

Map[Times @@ NextPrime[#, {0, 1, 2}] &, Select[Prime@ Range[360], AllTrue[{# + 2, # + 6}, PrimeQ] &]]

A163635 a(n) = 3*A022004(n) + 8.

Original entry on oeis.org

23, 41, 59, 131, 311, 329, 581, 689, 941, 1049, 1391, 1931, 2471, 2579, 2651, 3281, 3839, 3911, 4289, 4451, 4469, 4829, 5621, 5999, 6251, 6719, 6809, 7979, 8069, 9761, 10391, 10589, 11021, 11759, 12011, 12389, 13559, 13919, 14369, 14801

Offset: 1

Vincenzo Librandi, Aug 02 2009

Sum of the members of the n-th prime triple (p, p+2, p+6).

All terms are congruent to 5 (mod 18). See A242215. - Robert Bilinski, Sep 24 2019

			23 is in the sequence because 23 = 5+7+11 = 3*5+8.
41 is in the sequence because 41 = 11+13+17 = 3*11+8.

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

Cf. A022004, A073648, A098412.

Cf. A242215.

[(3*p+8): p in PrimesUpTo(1000)| IsPrime(p+6) and IsPrime(p+2)]; // Vincenzo Librandi, Jan 06 2018

8 + 3*Select[Prime[Range[1000]], PrimeQ[# + 2] && PrimeQ[# + 6] &] (* Vincenzo Librandi, Jan 04 2014 *)

is(n)=n%18==5 && isprime(n\3-2) && isprime(n\3) && isprime(n\3+4) \\ Charles R Greathouse IV, Jan 06 2018

a(n) = A022004(n) + (A022004(n)+2) + (A022004(n)+6);

a(n) = A022004(n) + A073648(n) + A098412(n).

Notation normalized by R. J. Mathar, Aug 07 2009

A277774 Decimal expansion of the prime triples constant, also known as Brun's constant B_{3a} = Sum (1/p + 1/(p+2) + 1/(p+6)) as p runs through the initial members of prime triples A022004.

Original entry on oeis.org

1, 0, 9, 7, 8, 5, 1, 0, 3, 9, 6, 7, 9

Offset: 1

Martin Renner, Oct 29 2016

			1.097851039679...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.14, p. 133.

Thomas R. Nicely, Prime Constellations Research Project (Mar 16 2010).

Cf. A022004, A065421, A194098, A213007, A277775.

Offset corrected by Rick L. Shepherd, Nov 03 2016

A007530 Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime.

Original entry on oeis.org

5, 11, 101, 191, 821, 1481, 1871, 2081, 3251, 3461, 5651, 9431, 13001, 15641, 15731, 16061, 18041, 18911, 19421, 21011, 22271, 25301, 31721, 34841, 43781, 51341, 55331, 62981, 67211, 69491, 72221, 77261, 79691, 81041, 82721, 88811, 97841, 99131

Offset: 1

N. J. A. Sloane, Robert G. Wilson v

nonn

Except for the first term, 5, all terms == 11 (mod 30). - Zak Seidov, Dec 04 2008
Some further values: For k = 1, ..., 10, a(k*10^3) = 11721791, 31210841, 54112601, 78984791, 106583831, 136466501, 165939791, 196512551, 230794301, 265201421. - M. F. Hasler, May 04 2009
k is the first prime of 2 consecutive twin prime pairs. - Daniel Forgues, Aug 01 2009
The prime quadruples of form p + (0, 2, 6, 8) have the quadruple congruence class (-1, +1, -1, +1) (mod 6). - Daniel Forgues, Aug 12 2009
s = (p+8)-(p) = 8 is the smallest s giving an admissible prime quadruple form, for which the only admissible form is p + (0, 2, 6, 8), since (0, 2, 6, 8) is the only form not covering all the congruence classes for any prime <= 4. Since s is smallest, these prime quadruples are prime constellations (or prime quadruplets), i.e., they contain consecutive primes. - Daniel Forgues, Aug 12 2009
Except for the first term, 5, all prime quadruples are of the form (15k-4, 15k-2, 15k+2, 15k+4), with k >= 1, and so are centered on 15k. - Daniel Forgues, Aug 12 2009
Subsequence of A022004. - R. J. Mathar, Feb 10 2013
The quadruplets are listed in A136162. - M. F. Hasler, Apr 20 2013
Starting at a(2) and examining the first 50 terms, (a(n)+4)/15 is a prime in 8 cases and a semiprime in 21; the last 18 terms have 2 primes and 11 semiprimes. Do the number of semiprimes continue to occur greater than mere chance? - J. M. Bergot, Apr 27 2015

			From _M. F. Hasler_, May 04 2009: (Start)
a(1)=5 is the start of the first prime quadruplet, {5,7,11,13}.
a(2)=11 is the start of the second prime quadruplet, {11,13,17,19}, and all other prime quadruplets differ from this one by a multiple of 30.
a(100)=470081 is the start of the 100th prime quadruplet;
a(500)=4370081 is the start of the 500th prime quadruplet.
a(167)=1002341 is the least quadruplet prime beyond 10^6. (End)

H. Rademacher, Lectures on Elementary Number Theory. Blaisdell, NY, 1964, p. 4.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Matt C. Anderson, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe).
C. K. Caldwell, The Prime Glossary, prime quadruple
Tony Forbes and Norman Luhn, prime k-tuplets
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
Norman Luhn, Table of n, a(n) for n = 1..1000000
Thomas R. Nicely, Enumeration to 1.6e15 of the prime quadruplets
H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics, Vol. 57, Birkhäuser, Boston, 1985, ISBN: 978-0-8176-8297-2, Chap. 4, see p. 65.
Eric Weisstein's World of Mathematics, Prime Quadruplet

Cf. A159910 (first differences divided by 30), A120120, A007811, A014561.

[ p: p in PrimesUpTo(11000)| IsPrime(p+2) and IsPrime(p+6) and IsPrime(p+8)] // Vincenzo Librandi, Nov 18 2010

A007530 = Select[Range[1, 10^5 - 1, 2], Union[PrimeQ[# + {0, 2, 6, 8}]] == {True} &] (* Alonso del Arte, Sep 24 2011 *)
Select[Prime[Range[10000]],AllTrue[#+{2,6,8},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 11 2019 *)

A007530( n, print_all=0, s=2 )={ my(p,q,r); until(!n--, until( p+8==s=nextprime(s+2), p=q; q=r; r=s); print_all && print1(p","));p} \\ The optional 3rd argument can be used to obtain large values by starting from some precomputed point instead of zero, using a(n+k) = A007530(k+1,,a(n)) (or A007530(k,,a(n)-1) for k>0); e.g., you get a(10^4+k) using A007530(k+1,,265201421) (value of a(10^4) from the comments section). - M. F. Hasler, May 04 2009

forprime(p=2, 10^5, if(isprime(p+2) && isprime(p+6) && isprime(p+8), print1(p, ", "))) \\ Felix Fröhlich, Jun 22 2014

from sympy import primerange
def aupto(limit):
  p, q, r, alst = 2, 3, 5, []
  for s in primerange(7, limit+9):
    if p+2 == q and p+6 == r and p+8 == s: alst.append(p)
    p, q, r = q, r, s
  return alst
print(aupto(10**5)) # Michael S. Branicky, May 11 2021

a(n) = 11 + 30*A014561(n-1) for n > 1. - M. F. Hasler, May 04 2009

More terms from Warut Roonguthai
Incorrect formula and Mathematica program removed by N. J. A. Sloane, Dec 04 2008, at the suggestion of Zak Seidov
Values up to a(1000) checked with the given PARI code by M. F. Hasler, May 04 2009

A022008 Initial member of prime sextuples (p, p+4, p+6, p+10, p+12, p+16).

Original entry on oeis.org

7, 97, 16057, 19417, 43777, 1091257, 1615837, 1954357, 2822707, 2839927, 3243337, 3400207, 6005887, 6503587, 7187767, 7641367, 8061997, 8741137, 10526557, 11086837, 11664547, 14520547, 14812867, 14834707, 14856757, 16025827, 16094707, 18916477, 19197247

Offset: 1

Warut Roonguthai

nonn

Without the initial 7, this gives primes at which difference pattern X42424Y (X and Y >= 8) occurs in A001223. - Labos Elemer
Subsequence of A022007. - Zak Seidov, Nov 01 2011
From Jean-Christophe Hervé, Sep 27 2014: (Start)
The primes in a sextuple a(n), a(n)+4, a(n)+6, a(n)+10, a(n)+12, a(n)+16 are consecutive since a(n)+2, a(n)+8 and a(n)+14 cannot be prime (multiple of 3).
The prime sextuples starting at a(n) give the highest concentration of primes that can occur on an interval of 17 integers (apart intervals starting at p < 7). It is conjectured that there are infinitely many such sextuples.
For n > 1, the 3 odd integers preceding and the 3 odd integers following the sextuple are not prime: a(n)-2 == a(n)+18 == 0 (mod 5), a(n)-4 == a(n)+20 == 0 (mod 3), a(n)-6 == a(n)+22 == 0 (mod 7) and thus a(n) == 97 (mod 210 = 2*3*5*7). (End)
All terms are congruent to 7 (mod 30). - Zak Seidov, May 07 2017
All terms but the first one are congruent to 97 (mod 210). - M. F. Hasler, Jan 18 2022

			n=2: 97, 101, 103, 107, 109, 113 are consecutive primes, while 91, 93, 95 and 115, 117 and 119 are not (cf. 4th comment about the border of composites).

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Zak Seidov)
T. Forbes and Norman Luhn, Prime k-tuplets
R. J. Mathar, Table of Prime Gap Constellations

Cf. A022007.
Cf. A001223, A052162, A052163, A052164, A052165, A052166, A052167, A052168, A047078.
Cf. A350826 (number of n-digit terms).

P:=Filtered([1,3..2*10^7+1],IsPrime);;  I:=[4,2,4,2,4];;
P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;
A022008:=List(Positions(List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3],P1[i+4]]),I),j->P[j]); # Muniru A Asiru, Sep 03 2017

[p: p in PrimesUpTo(2*10^7) | IsPrime(p+4) and IsPrime(p+6) and IsPrime(p+10)and IsPrime(p+12) and IsPrime(p+16)]; // Vincenzo Librandi, Aug 23 2015

for i from 1 to 2*10^5 do if [ithprime(i+1), ithprime(i+2), ithprime(i+3), ithprime(i+4), ithprime(i+5)] = [ithprime(i)+4,ithprime(i)+6,ithprime(i)+10,ithprime(i)+12,ithprime(i)+16] then print(ithprime(i)); fi; od; # Muniru A Asiru, Sep 03 2017

lst = {}; Do[p = Prime[n]; If[PrimeQ[p+4] && PrimeQ[p+6] && PrimeQ[p+10] && PrimeQ[p+12] && PrimeQ[p+16], AppendTo[lst, p]], {n, 1000000}]; lst
Transpose[Select[Partition[Prime[Range[10^6]],6,1],Differences[#]=={4,2,4,2,4}&]][[1]] (* Harvey P. Dale, Mar 15 2015 *)

p=2;q=3;r=5;s=7;t=11;forprime(u=13,1e9,if(u-p==16 && p%3==1, print1(p", "));p=q;q=r;r=s;s=t;t=u) \\ Charles R Greathouse IV, Mar 29 2013

{next_A022008(p, L=Vec(p+1,5), m=210, r=Mod(97,m))=for(i=1,oo, L[i%5+1]+16==(p=nextprime(p+1))&&break; p%m>111 && until(r==p=nextprime((p+8)\/210*210+97),); L[i%5+1]=p); p-16} \\ M. F. Hasler, Jan 18 2022

use ntheory ":all"; say for sieve_prime_cluster(1,1e8, 4,6,10,12,16); # Dana Jacobsen, Sep 30 2015

A007529 Prime triples: p; p+2 or p+4; p+6 all prime.

Original entry on oeis.org

5, 7, 11, 13, 17, 37, 41, 67, 97, 101, 103, 107, 191, 193, 223, 227, 277, 307, 311, 347, 457, 461, 613, 641, 821, 823, 853, 857, 877, 881, 1087, 1091, 1277, 1297, 1301, 1423, 1427, 1447, 1481, 1483, 1487, 1607, 1663, 1693, 1783, 1867, 1871, 1873, 1993, 1997

Offset: 1

N. J. A. Sloane, Robert G. Wilson v

nonn

Or, prime(m) such that prime(m+2) = prime(m)+6. - Zak Seidov, May 07 2012

H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see p. 65.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Zak Seidov, Table of n, a(n) for n = 1..10000
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Cf. A031924, A023201, A098414, A098415, A098424, A098416, A098417.

Union of A022004 and A022005.

[NthPrime(n): n in [1..310] | (NthPrime(n)+6) eq NthPrime(n+2)]; // Bruno Berselli, May 07 2012

N:= 10000: # to get all terms <= N
Primes:= select(isprime, [seq(2*i+1, i=1..floor((N+5)/2))]):locs:= select(t -> Primes[t+2]-Primes[t]=6, [$1..nops(Primes)-2]):
Primes[locs]; # Robert Israel, Apr 30 2015

ptrsQ[n_]:=PrimeQ[n+6]&&(PrimeQ[n+2]||PrimeQ[n+4])
Select[Prime[Range[400]],ptrsQ]  (* Harvey P. Dale, Mar 08 2011 *)

p=2;q=3;forprime(r=5,1e4,if(r-p==6,print1(p", "));p=q;q=r) \\ Charles R Greathouse IV, May 07 2012

a(n) = A098415(n) - 6. - Zak Seidov, Apr 30 2015

A257124 Initial members of prime septuplets.

Original entry on oeis.org

11, 5639, 88799, 165701, 284729, 626609, 855719, 1068701, 1146779, 6560999, 7540439, 8573429, 11900501, 15760091, 17843459, 18504371, 19089599, 21036131, 24001709, 25658441, 39431921, 42981929, 43534019, 45002591, 67816361, 69156539, 74266259, 79208399, 80427029, 84104549, 86818211, 87988709, 93625991, 124066079

Offset: 1

Tim Johannes Ohrtmann, Apr 16 2015

nonn

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..1990
Tony Forbes, k-tuplets

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: this sequence out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.
Cf. A343637 (distance from 10^n to the next septuplet).
Cf. A100418.

Disjoint union of A022009 and A022010. - M. F. Hasler, Aug 04 2021

A078847 Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <= 6 (i.e., when d = 2, 4 or 6) and forming pattern = [2, 4, 6]; short notation = [246] d-pattern.

Original entry on oeis.org

17, 41, 227, 347, 641, 1091, 1277, 1427, 1487, 1607, 2687, 3527, 3917, 4001, 4127, 4637, 4787, 4931, 8231, 9461, 10331, 11777, 12107, 13901, 14627, 20747, 21557, 23741, 25577, 26681, 26711, 27737, 27941, 28277, 29021, 31247, 32057, 32297

Offset: 1

Labos Elemer, Dec 11 2002

nonn

Subsequence of A022004. - R. J. Mathar, Feb 10 2013

a(n) + 12 is the greatest term in the sequence of 4 consecutive primes with 3 consecutive gaps 2, 4, 6. - Muniru A Asiru, Aug 03 2017

			17, 17+2 = 19, 17+2+4 = 23, 17+2+4+6 = 29 are consecutive primes.

Zak Seidov, Table of n, a(n) for n = 1..2000

Cf. analogous prime quadruple sequences with various possible {2, 4, 6}-difference-patterns in brackets: A007530[242], A078847[246], A078848[264], A078849[266], A052378[424], A078850[426], A078851[462], A078852[466], A078853[624], A078854[626], A078855[642], A078856[646], A078857[662], A078858[664], A033451[666].

Cf. A190814[2,4,6,8], A190817[2,4,6,8,10], A190819[2,4,6,8,10,12], A190838[2,4,6,8,10,12,14]

d = Differences[Prime[Range[10000]]]; Prime[Flatten[Position[Partition[d, 3, 1], {2, 4, 6}]]] (* T. D. Noe, May 23 2011 *)
Transpose[Select[Partition[Prime[Range[10000]],4,1],Differences[#] == {2,4,6}&]][[1]] (* Harvey P. Dale, Aug 07 2013 *)

Primes p=prime(i) such that prime(i+1) = p+2, prime(i+2) = p+2+4, prime(i+3) = p+2+4+6.

Listed terms verified by Ray Chandler, Apr 20 2009

Additional cross references from Harvey P. Dale, May 10 2014

A257125 Initial members of prime 9-tuplets (or nonuplets).

Original entry on oeis.org

7, 11, 13, 17, 1277, 88789, 113143, 113147, 855709, 74266249, 182403491, 226449521, 252277007, 408936947, 521481197, 626927443, 910935911, 964669609, 1042090781, 1116452627, 1209950867, 1422475909, 1459270271, 1645175087, 2117861719, 2335215973, 2558211559, 2843348351, 2873599429, 2966003057, 3447123283, 3947480417

Offset: 1

Tim Johannes Ohrtmann, Apr 16 2015

nonn

Primes prime(m) such that prime(m+8) = prime(m) + 30. - Zak Seidov, Jul 06 2015

Zak Seidov, Table of n, a(n) for n = 1..651 (Essentially original b-file by Tim Johannes Ohrtmann, just added a(1)=7 and corrected EndOfFile)
Tony Forbes and Norman Luhn, Smallest Prime k-tuplets

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: this sequence out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

[NthPrime(n): n in [0..2*10^4] | NthPrime(n+8) eq (NthPrime(n) + 30)]; // Vincenzo Librandi, Jul 08 2015

{p, q, r, s, t, u, v, w, x} = Prime@ Range@ 9; lst = {}; While[p < 1000000001, If[p + 30 == x, AppendTo[lst, p]; Print@ p]; {p, q, r, s, t, u, v, w, x} = {q, r, s, t, u, v, w, x, NextPrime@ x}]; lst (* Robert G. Wilson v, Jul 06 2015 *)
Select[Partition[Prime[Range[5 10^6]],9,1],#[[1]]+30==#[[9]]&][[;;,1]] (* The program generates the first 10 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Jul 01 2024 *)

main(size)=v=vector(size); i=0; m=1; while(iAnders Hellström, Jul 08 2015

A257127 Initial members of prime 10-tuplets (or decaplets).

Original entry on oeis.org

11, 9853497737, 21956291867, 22741837817, 33081664151, 83122625471, 164444511587, 179590045487, 217999764107, 231255798857, 242360943257, 294920291201, 573459229151, 663903555851, 666413245007, 688697679401, 696391309697, 730121110331, 867132039857, 974275568237, 976136848847, 1002263588297

Offset: 1

Tim Johannes Ohrtmann, Apr 16 2015

nonn

M. F. Hasler, Table of n, a(n) for n = 1..10000 (first 101 terms from Tim Johannes Ohrtmann), Mar 01 2022
Tony Forbes and Norman Luhn Prime k-tuplets
Norman Luhn, The big database of "The smallest prime k-tuplets", section "10-tuplets": up to 10^20 as of March 2022.

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime quintuplets: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: this sequence out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

cp's OEIS Frontend

A372319 Products of prime triples (p, p+2, p+6) where p = A022004(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A163635 a(n) = 3*A022004(n) + 8.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions

A277774 Decimal expansion of the prime triples constant, also known as Brun's constant B_{3a} = Sum (1/p + 1/(p+2) + 1/(p+6)) as p runs through the initial members of prime triples A022004.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Extensions

A007530 Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Magma

Mathematica

PARI

PARI

Python

Formula

Extensions

A022008 Initial member of prime sextuples (p, p+4, p+6, p+10, p+12, p+16).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

PARI

Perl

A007529 Prime triples: p; p+2 or p+4; p+6 all prime.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI