A176114 -id:A176114 - cp's OEIS frontend

A075749 Numbers k such that 210*k +- 1 are twin primes.

2, 5, 11, 13, 16, 28, 29, 30, 35, 36, 42, 44, 50, 51, 55, 57, 73, 86, 104, 121, 125, 128, 135, 140, 147, 148, 157, 158, 160, 161, 165, 168, 179, 193, 204, 205, 209, 223, 244, 247, 249, 251, 255, 264, 271, 273, 277, 281, 282, 290, 302, 304, 310, 312, 313, 316

Offset: 1

Zak Seidov, Oct 08 2002

			k = 2 is a term since 210*2 - 1 = 419 and 210*2 + 1 = 421 are twin primes.

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

Cf. A002822 (with 6*k +- 1), A176114 (with 30*k +- 1).

[k:k in [1..320]| IsPrime(210*k-1) and IsPrime(210*k+1)]; // Marius A. Burtea, Jan 01 2020

Select[Range[6! ],PrimeQ[210*#-1]&&PrimeQ[210*#+1]&] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2010 *)

isok(n) = isprime(210*n+1) && isprime(210*n-1); \\ Michel Marcus, Jan 14 2015

A216847 Integers n such that 6n -/+ 1 and 30n -/+ 1 are all primes.

Original entry on oeis.org

1, 2, 5, 77, 100, 110, 135, 170, 215, 338, 357, 385, 390, 467, 555, 593, 597, 688, 737, 758, 980, 1127, 1682, 1743, 1785, 2305, 2555, 3152, 3372, 3640, 3927, 3985, 4375, 4480, 4597, 4615, 4653, 4685, 5082, 5252, 5357, 5558, 6018, 6078, 6088, 6155, 7012, 7380

Offset: 1

Zak Seidov, Dec 10 2012

nonn

Consider two primes P=2p+3q, Q=2q+3p with p and q twin primes, and p=6n-1, then P=Q+2, and sequence gives corresponding values of n.

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

Intersection of A002822 and A176114.

Select[Range[10000], PrimeQ[6 # - 1] && PrimeQ[6 # + 1] && PrimeQ[30 # - 1] && PrimeQ[30 # + 1] &] (* T. D. Noe, Dec 10 2012 *)
Select[Range[8000],AllTrue[Flatten[{6#+{1,-1},30#+{1,-1}}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 23 2014 *)

{for(n=1,6000,if(isprime(p=6*n-1)&&isprime(p+2)&&isprime(q=30*n-1)&&isprime(q+2),print1(n",")))}

A331840 Numbers k such that 30k-13, 30k-11 are twin primes.

Original entry on oeis.org

1, 4, 5, 7, 8, 12, 21, 28, 29, 43, 48, 50, 54, 56, 57, 60, 63, 67, 68, 70, 75, 76, 89, 90, 106, 109, 116, 118, 119, 126, 131, 138, 139, 141, 145, 151, 152, 155, 160, 166, 181, 183, 189, 196, 207, 228, 232, 238, 244, 249, 250, 252, 259, 263, 270, 280, 285, 287

Offset: 1

Frank Ellermann, Feb 26 2020

All twin primes > 7 have the form 30*k-{13,11}, or 30*k +-1 (A176114), or 30*k+{11,13} (A089160).
All twin primes > 7 with least significant decimal digit 7 have the form 30*k-13.
All twin primes > 7 with least significant decimal digit 3 have the form 30*k+13.

			1 is a term because 1*30 - 13 =  17 = prime(6)  and 1*30 - 11 =  19 = prime(7).
4 is a term because 4*30 - 13 = 107 = prime(28) and 4*30 - 11 = 109 = prime(29).
5 is a term because 5*30 - 13 = 137 = prime(33) and 5*30 - 11 = 139 = prime(34).

Cf. A089160, A089161, A176114, A332772.

Cf. A000040, A001097, A002822, A132242, A282323, A282324.

Select[Range[300], And @@ PrimeQ[30*# - {11, 13}] &] (* Amiram Eldar, Feb 29 2020 *)

isok(k) = isprime(30*k-13) && isprime(30*k-11); \\ Michel Marcus, Feb 29 2020

S = 1
do N = 2 while length( S ) < 255
   if NOPRIME( N*30 -13 )  then  iterate N
   if NOPRIME( N*30 -11 )  then  iterate N
   S = S || ',' N
end N
say S

a(n) = A089161(n)+1.

A332772 Numbers k > 0 such that 30k +- 7 is prime.

Original entry on oeis.org

1, 2, 3, 4, 9, 10, 12, 13, 15, 19, 20, 25, 26, 29, 32, 33, 37, 41, 43, 48, 52, 53, 54, 58, 66, 67, 76, 78, 81, 85, 88, 89, 90, 92, 95, 97, 101, 107, 118, 120, 121, 128, 129, 134, 143, 150, 153, 155, 165, 166, 172, 178, 180, 194, 195, 202, 207, 209, 211, 212

Offset: 1

Frank Ellermann, Feb 25 2020

Looking for prime factors > 5=prime(3) in 8=A005867(3) candidates mod 30=A002110(3) two candidates in the form 30k +- 7 with k > 0 never belong to a twin prime pair. Twin primes can be (30k-13, 30k-11) A331840, (30k-1, 30k +1) A176114, or (30k+11, 30k+13) A089160.

			a(4)=4 for prime(30)=113=4*30-7 and prime(31)=127=4*30+7.
a(5)=9 for prime(56)=263=9*30-7 and prime(59)=277=9*30+7.

Frank Ellermann, Illustration for A002110, A005867, A038110, A060753

Cf. A000040, A002110, A005867, A089160, A176114, A331840.

Subsequence of A158573. Prime pairs 30k +- 7 in A329262.

Select[Range@ 215, AllTrue[30 # + {-7, 7}, PrimeQ] &] (* Michael De Vlieger, Feb 25 2020 *)

S = 1
do N = 2 while length( S ) < 255
   if NOPRIME( N * 30 + 7 )   then  iterate N
   if NOPRIME( N * 30 - 7 )   then  iterate N
   S = S || ',' N
end N
say S

A359184 Numbers k such that 30k - 1, 30k + 1, 30k^2 - 1 and 30k^2 + 1 are all prime.

Original entry on oeis.org

1, 14, 118, 232, 538, 720, 1155, 1253, 2821, 3151, 6161, 6238, 6916, 7428, 7827, 9009, 9521, 9933, 10284, 10779, 11661, 12348, 13663, 13811, 14092, 14938, 15273, 16323, 16457, 17116, 17940, 20735, 21931, 22022, 24010, 24311, 24375, 26557, 28293, 29645, 30555, 33880, 34033, 34328, 35797, 36413

Offset: 1

Robert Israel, Dec 18 2022

nonn

Numbers k such that 30*k and 30*k^2 are in A014574.

The first number k > 1 such that 30*k - 1, 30*k + 1, 30*k^2 - 1, 30*k^2 + 1, 30*k^3 - 1 and 30*k^3 + 1 are all prime is 266225.

			a(2) = 14 is a term because 30*14 - 1 = 419, 30*14 + 1 = 421, 30*14^2 - 1 = 5879, and 30*14^2 + 1 = 5881 are all prime.

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

Cf. A014574.

Intersection of A176114 and A283867.

select(k -> isprime(30*k-1) and isprime(30*k+1) and isprime(30*k^2-1) and isprime(30*k^2+1), [$1..10^5]);

Select[Range[40000], AllTrue[{30*# - 1, 30*# + 1, 30*#^2 - 1, 30*#^2 + 1}, PrimeQ] &] (* Amiram Eldar, Dec 19 2022 *)

A176115 Numbers n such that 2310n-1, 2310n+1 are twin primes, (2310=235711).

Original entry on oeis.org

1, 4, 5, 11, 15, 19, 24, 34, 40, 48, 51, 58, 66, 73, 78, 97, 98, 100, 106, 109, 116, 117, 123, 129, 130, 134, 136, 137, 143, 163, 169, 175, 176, 180, 182, 186, 194, 201, 207, 222, 226, 228, 234, 239, 248, 271, 274, 275, 279, 285, 286, 295, 305, 313, 320, 347

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 08 2010

nonn

Cf. A002822, A075749, A154114, A176114

Select[Range[6! ],PrimeQ[2310*#-1]&&PrimeQ[2310*#+1]&]

cp's OEIS Frontend

A075749 Numbers k such that 210*k +- 1 are twin primes.

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Magma

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A216847 Integers n such that 6n -/+ 1 and 30n -/+ 1 are all primes.

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A331840 Numbers k such that 30*k-13, 30*k-11 are twin primes.

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A332772 Numbers k > 0 such that 30k +- 7 is prime.

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A359184 Numbers k such that 30*k - 1, 30*k + 1, 30*k^2 - 1 and 30*k^2 + 1 are all prime.

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Maple

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A176115 Numbers n such that 2310*n-1, 2310*n+1 are twin primes, (2310=2*3*5*7*11).

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Mathematica

A331840 Numbers k such that 30k-13, 30k-11 are twin primes.

A359184 Numbers k such that 30k - 1, 30k + 1, 30k^2 - 1 and 30k^2 + 1 are all prime.

A176115 Numbers n such that 2310n-1, 2310n+1 are twin primes, (2310=235711).