A124519 -id:A124519 - cp's OEIS frontend

A124518 Numbers k such that 10k-1 and 10k+1 are twin primes.

3, 6, 15, 18, 24, 27, 42, 57, 60, 66, 81, 102, 105, 123, 129, 132, 162, 195, 213, 231, 234, 255, 273, 279, 297, 300, 312, 330, 333, 336, 339, 354, 393, 402, 405, 423, 426, 465, 480, 501, 510, 528, 552, 564, 585, 588, 609, 627, 630, 636, 645, 657, 666, 669, 678

Offset: 1

Artur Jasinski, Nov 04 2006

nonn

All terms are divisible by 3. - Robert Israel, Apr 07 2019

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

Cf. A040040, A045753, A002822, A124065, A124519-A124522, A063983.

select(t -> isprime(10*t+1) and isprime(10*t-1), [seq(i,i=3..1000,3)]); # Robert Israel, Apr 07 2019

Select[Range[678], And @@ PrimeQ[{-1, 1} + 10# ] &] (* Ray Chandler, Nov 16 2006 *)

A124065 Numbers k such that 8k - 1 and 8k + 1 are twin primes.

Original entry on oeis.org

9, 24, 30, 39, 54, 75, 129, 144, 165, 186, 201, 234, 261, 264, 324, 336, 339, 375, 390, 396, 420, 441, 459, 471, 516, 534, 600, 621, 654, 660, 690, 705, 735, 795, 819, 849, 870, 891, 936, 945, 1011, 1029, 1125, 1155, 1179, 1215, 1221, 1251, 1284, 1395, 1419

Offset: 1

Artur Jasinski, Nov 04 2006

nonn

			9 is in the sequence since 8*9 - 1 = 71 and 8*9 + 1 = 73 are twin primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A005122 and A005123.

Cf. A040040, A045753, A002822, A124518, A124519, A124520, A124521, A124522, A063983.

[n: n in [1..2000] | IsPrime(8*n+1) and IsPrime(8*n-1)] // Vincenzo Librandi, Mar 08 2010

Select[Range[1500], And @@ PrimeQ[{-1, 1} + 8# ] &] (* Ray Chandler, Nov 16 2006 *)

from sympy import isprime
def ok(n): return isprime(8*n - 1) and isprime(8*n + 1)
print(list(filter(ok, range(1420)))) # Michael S. Branicky, Sep 24 2021

Extended by Ray Chandler, Nov 16 2006

A135368 a(n) = (nextprime(12n) - previousprime(12n))/2.

Original entry on oeis.org

1, 3, 3, 3, 1, 1, 3, 4, 1, 7, 3, 5, 3, 3, 1, 1, 6, 6, 1, 1, 3, 3, 3, 5, 7, 1, 7, 3, 1, 4, 3, 3, 4, 4, 1, 1, 3, 4, 6, 4, 4, 3, 6, 9, 9, 5, 3, 3, 3, 1, 3, 6, 5, 3, 1, 6, 4, 5, 4, 4, 3, 4, 3, 4, 7, 5, 6, 5, 1, 7, 7, 7, 7, 10, 10, 4, 5, 4, 3, 7, 3, 4, 3, 6, 1, 1, 5, 5, 3, 9, 1, 3, 4, 3, 11, 1, 4, 5, 3, 4, 6, 3, 3, 6

Offset: 1

Zak Seidov, Feb 17 2008

nonn

a(n)=1 if 12n -/+ 1 are twin primes. Corresponding n's are in A124519: 1,5,6,9,15,16,19,20,26,29,35,36,50,...

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A124519, A135023.

Table[ ( NextPrime[12*n, 1] - NextPrime[12*n, -1] )/2, {n, 1, 25}] (* G. C. Greubel, Oct 11 2016 *)

a(n) = (nextprime(12*n) - precprime(12*n))/2; \\ Michel Marcus, Oct 12 2016

A137877 Numbers k such that 18k - 1 and 18k + 1 are twin primes.

Original entry on oeis.org

1, 4, 6, 10, 11, 15, 24, 29, 45, 46, 49, 59, 64, 71, 90, 104, 111, 116, 119, 126, 130, 144, 155, 165, 176, 181, 185, 196, 199, 204, 214, 225, 231, 235, 241, 249, 251, 266, 274, 276, 279, 301, 314, 319, 325, 326, 350, 364, 365, 370, 386, 396, 406, 416, 420, 431

Offset: 1

Zak Seidov, Feb 19 2008

nonn

			1 is in the sequence since 18*1 - 1 = 17 and 18*1 + 1 = 19 are twin primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A124519, A135023, A135368, A137876.

q=18; lst={}; Do[r=n*q; If[PrimeQ[r-1]&&PrimeQ[r+1], AppendTo[lst, n]], {n, 1, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)

A124520 Numbers k such that 14k - 1 and 14k + 1 are twin primes.

Original entry on oeis.org

3, 30, 33, 63, 75, 78, 93, 102, 123, 138, 153, 162, 165, 192, 195, 240, 252, 273, 297, 303, 342, 387, 393, 420, 435, 438, 450, 468, 483, 522, 525, 540, 588, 630, 633, 660, 663, 717, 738, 747, 750, 765, 798, 825, 837, 855, 957, 978, 993, 1023, 1032, 1062

Offset: 1

Artur Jasinski, Nov 04 2006

nonn

			3 is in the sequence since 14*3 - 1 = 41 and 14*3 + 1 = 43 are twin primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A040040, A045753, A002822, A124065, A124518, A124519, A124521, A124522, A063983.

Select[Range[1100], And @@ PrimeQ[{-1, 1} + 14# ] &] (* Ray Chandler, Nov 16 2006 *)

Extended by Ray Chandler, Nov 16 2006

A124521 Numbers k such that 16k - 1 and 16k + 1 are twin primes.

Original entry on oeis.org

12, 15, 27, 72, 93, 117, 132, 162, 168, 195, 198, 210, 258, 267, 300, 327, 330, 345, 435, 468, 642, 765, 813, 855, 903, 912, 960, 978, 993, 1128, 1143, 1182, 1290, 1350, 1353, 1365, 1392, 1398, 1440, 1632, 1680, 1713, 1737, 1797, 1848, 1860, 1947, 1953, 1962

Offset: 1

Artur Jasinski, Nov 04 2006

nonn

			12 is in the sequence since 16*12 - 1 = 191 and 16*12 + 1 = 193 are twin primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A040040, A045753, A002822, A124065, A124518, A124519, A124520, A124522, A063983.

A124521:=n->`if`(isprime(16*n-1) and isprime(16*n+1), n, NULL): seq(A124521(n), n=1..2000); # Wesley Ivan Hurt, Oct 10 2014

Select[Range[2000], And @@ PrimeQ[{-1, 1} + 16# ] &] (* Ray Chandler, Nov 16 2006 *)

Extended by Ray Chandler, Nov 16 2006

A137876 a(n) = (nextprime(18n)-previousprime(18n))/2.

Original entry on oeis.org

1, 3, 3, 1, 4, 1, 7, 5, 3, 1, 1, 6, 3, 3, 1, 5, 7, 7, 5, 4, 3, 4, 5, 1, 4, 6, 4, 3, 1, 9, 3, 3, 3, 3, 6, 3, 6, 4, 4, 4, 3, 3, 7, 5, 1, 1, 7, 7, 1, 10, 4, 4, 7, 3, 4, 6, 5, 5, 1, 9, 3, 4, 11, 1, 4, 3, 6, 3, 6, 9, 1, 3, 6, 17, 17, 3, 9, 5, 7, 4, 3, 5, 3, 6, 4, 3, 4, 7, 3, 1, 10, 10, 12, 12, 6, 5, 3, 9, 3, 6, 6

Offset: 1

Zak Seidov, Feb 19 2008

nonn

a(n)=1 if 18n -/+ 1 are twin primes. Corresponding n's are in A137877.

Note that a(n) cannot be 2 (because, for arbitrary number m, if (6*m-1) is prime then (6*m+3) is not, and similarly, if (6*m+1) is prime then (6*m-3) is not). I conjecture that all other values are possible and a(n) == 0 (mod 3) are (much) more abundant.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A124519, A135023, A135368, A137877.

[(NextPrime(18*n)-PreviousPrime(18*n))/2: n in [1..100]]; // Vincenzo Librandi, Apr 19 2015

seq((nextprime(18*n)-prevprime(18*n))/2, n=1..100); # Robert Israel, Apr 19 2015

Table[(NextPrime[18 n] - NextPrime[18 n, -1]) / 2, {n, 100}] (* Vincenzo Librandi, Apr 19 2015 *)

a(n) = (nextprime(18*n) - precprime(18*n))/2; \\ Michel Marcus, Oct 13 2013

A137920 Numbers k such that 24k-1 and 24k+1 are twin primes.

Original entry on oeis.org

3, 8, 10, 13, 18, 25, 43, 48, 55, 62, 67, 78, 87, 88, 108, 112, 113, 125, 130, 132, 140, 147, 153, 157, 172, 178, 200, 207, 218, 220, 230, 235, 245, 265, 273, 283, 290, 297, 312, 315, 337, 343, 375, 385, 393, 405, 407, 417, 428, 465, 473, 493, 503, 510, 542

Offset: 1

Zak Seidov, Feb 23 2008

nonn

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

Cf. A124519, A135023, A135368, A137876, A137877, A137919.

[n: n in [1..600] | IsPrime(24*n+1) and IsPrime(24*n-1)] // Vincenzo Librandi, Feb 12 2018

select(t -> isprime(24*t-1) and isprime(24*t+1), [$1..1000]); # Robert Israel, Feb 11 2018

q=24; lst={}; Do[r=n*q; If[PrimeQ[r-1]&&PrimeQ[r+1], AppendTo[lst, n]], {n, 1, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)
Select[Range[600], PrimeQ[24 # - 1] && PrimeQ[24 # + 1] &] (* Vincenzo Librandi, Feb 12 2018 *)

isok(k) = isprime(24*k-1) && isprime(24*k+1); \\ Michel Marcus, Feb 12 2018

A137919 (Nextprime(24n)-previousprime(24n))/2.

Original entry on oeis.org

3, 3, 1, 4, 7, 5, 3, 1, 6, 1, 3, 5, 1, 3, 4, 3, 4, 1, 4, 4, 3, 9, 5, 3, 1, 6, 3, 6, 5, 4, 4, 4, 5, 5, 7, 7, 10, 4, 4, 7, 4, 6, 1, 5, 9, 3, 3, 1, 5, 4, 3, 6, 9, 3, 1, 17, 3, 9, 7, 4, 6, 1, 6, 6, 4, 7, 1, 5, 10, 12, 5, 5, 3, 9, 6, 4, 7, 1, 6, 9, 8, 11, 3, 3, 7, 3, 1, 1, 3, 4, 12, 3, 8, 8, 4, 6, 11, 3, 3, 6, 7, 6

Offset: 1

Zak Seidov, Feb 23 2008

nonn

a(n)=1 if 24n -/+ 1 are twin primes.

Corresponding n's are in A137920.

Cf. A124519, A135023, A135368, A137876, A137877, A137920.

Table[(NextPrime[24n]-NextPrime[24n,-1])/2,{n,110}] (* Harvey P. Dale, Apr 15 2015 *)

a(n) = (nextprime(24*n) - precprime(24*n))/2; \\ Michel Marcus, Oct 13 2013

A174372 Numbers k such that 12k - 5, 12k - 1, 12k + 1, and 12k + 5 are primes.

Original entry on oeis.org

1, 9, 19, 26, 91, 119, 124, 156, 224, 399, 436, 471, 569, 691, 1141, 1311, 1339, 1349, 1449, 1619, 1729, 1969, 2009, 2616, 2779, 2961, 3001, 3166, 3369, 3649, 3689, 6641, 6834, 7191, 7401, 7544, 7791, 7924, 8426, 8461, 9214, 9291, 9429, 9431, 9744

Offset: 1

Juri-Stepan Gerasimov, Mar 17 2010

			1 is a term because 1*12-5=7, 1*12-1=11, 1*12+1=13, and 1*12+5=17 are all prime.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A124519.

Select[Range[10^4], AllTrue[12# + {-5, -1, 1, 5}, PrimeQ] &] (* Amiram Eldar, Dec 17 2019 *)

Extended by Charles R Greathouse IV, Mar 18 2010

cp's OEIS Frontend

A124518 Numbers k such that 10k-1 and 10k+1 are twin primes.

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A124065 Numbers k such that 8*k - 1 and 8*k + 1 are twin primes.

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A135368 a(n) = (nextprime(12*n) - previousprime(12*n))/2.

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A137877 Numbers k such that 18*k - 1 and 18*k + 1 are twin primes.

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A124520 Numbers k such that 14*k - 1 and 14*k + 1 are twin primes.

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A124521 Numbers k such that 16*k - 1 and 16*k + 1 are twin primes.

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A137876 a(n) = (nextprime(18n)-previousprime(18n))/2.

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Magma

Maple

Mathematica

PARI

A137920 Numbers k such that 24*k-1 and 24*k+1 are twin primes.

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A124065 Numbers k such that 8k - 1 and 8k + 1 are twin primes.

A135368 a(n) = (nextprime(12n) - previousprime(12n))/2.

A137877 Numbers k such that 18k - 1 and 18k + 1 are twin primes.

A124520 Numbers k such that 14k - 1 and 14k + 1 are twin primes.

A124521 Numbers k such that 16k - 1 and 16k + 1 are twin primes.

A137920 Numbers k such that 24k-1 and 24k+1 are twin primes.

A174372 Numbers k such that 12k - 5, 12k - 1, 12k + 1, and 12k + 5 are primes.