A063983 -id:A063983 - cp's OEIS frontend

1, 3, 15, 18, 27, 45, 48, 57, 60, 78, 87, 105, 108, 150, 165, 207, 255, 258, 273, 288, 330, 357, 363, 372, 402, 405, 417, 447, 468, 483, 507, 522, 528, 567, 585, 648, 672, 678, 750, 780, 792, 813, 825, 840, 843, 867, 882, 885, 918, 942, 963, 1005, 1023

Offset: 1

Felice Russo

			3 belongs to the sequence because 4*3+1 and 4*3-1 are both primes.

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

Cf. A040040, A002822, A124065, A124518-A124522, A063983.

[n: n in [1..2000] | IsPrime(4*n+1) and IsPrime(4*n-1)] // Vincenzo Librandi, Nov 18 2010

Select[Range[1023], And @@ PrimeQ[{-1, 1} + 4# ] &] (* Ray Chandler, Dec 06 2006 *)

list(lim)=my(v=List(),p=2); forprime(q=3,4*lim+1, if(q-p==2 && p%4==3, listput(v,q\4)); p=q); Vec(v) \\ Charles R Greathouse IV, Dec 03 2016

More terms from Erich Friedman

A124519 Numbers k such that 12k - 1 and 12k + 1 are twin primes.

Original entry on oeis.org

1, 5, 6, 9, 15, 16, 19, 20, 26, 29, 35, 36, 50, 55, 69, 85, 86, 91, 96, 110, 119, 121, 124, 134, 135, 139, 149, 156, 161, 169, 174, 176, 189, 195, 216, 224, 226, 250, 260, 264, 271, 275, 280, 281, 289, 294, 295, 306, 314, 321, 335, 341, 344, 355, 356, 379, 399

Offset: 1

Artur Jasinski, Nov 04 2006

nonn

			1 is in the sequence since 12*1 - 1 = 11 and 12*1 + 1 = 13 are twin primes.

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

Cf. A040040, A045753, A002822, A124065, A124518, A124520, A124521, A124522, A063983.

Select[Range[400], And @@ PrimeQ[{-1, 1} + 12# ] &] (* Ray Chandler, Nov 16 2006 *)

Extended by Ray Chandler, Nov 16 2006

A124522 a(n) = smallest k such that 2nk-1 and 2nk+1 are primes.

Original entry on oeis.org

2, 1, 1, 9, 3, 1, 3, 12, 1, 3, 9, 3, 12, 15, 1, 6, 3, 2, 6, 6, 1, 15, 3, 4, 3, 6, 2, 48, 6, 1, 21, 3, 3, 15, 6, 1, 27, 3, 4, 3, 15, 5, 12, 15, 2, 9, 3, 2, 9, 6, 1, 3, 60, 1, 6, 24, 2, 3, 9, 2, 129, 12, 7, 9, 15, 5, 12, 27, 1, 3, 9, 3, 42, 45, 1, 90, 3, 2, 66, 21, 5, 63, 27, 16, 6, 6, 2, 12, 24, 1, 6

Offset: 1

Artur Jasinski, Nov 04 2006

nonn

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

Cf. A040040, A045753, A002822, A124065, A124518-A124522, A063983.

isA001359 := proc(n) RETURN( isprime(n) and isprime(n+2)) ; end: A124522 := proc(n) local k; k :=1 ; while true do if isA001359(2*n*k-1) then RETURN(k) ; fi ; k := k+1 ; od ; end: for n from 1 to 60 do printf("%d,",A124522(n)) ; od ; # R. J. Mathar, Nov 06 2006

f[n_] := Block[{k = 1},While[Nand @@ PrimeQ[{-1, 1} + 2n*k], k++ ];k];Table[f[n], {n, 91}] (* Ray Chandler, Nov 16 2006 *)
skp[n_]:=Module[{k=1},While[AnyTrue[2n k+{1,-1},CompositeQ],k++];k]; Join[{2},Array[skp,100,2]] (* Harvey P. Dale, Mar 30 2024 *)

{for(n=1,91,k=1;while(!isprime(2*n*k-1)||!isprime(2*n*k+1),k++);print1(k, ","))}

Edited and extended by Klaus Brockhaus and R. J. Mathar, Nov 06 2006

A071576 a(n) = least k such that 2ik + 1 is prime for all 1 <= i <= n.

Original entry on oeis.org

1, 1, 1, 165, 5415, 12705, 256410, 256410, 6480303060, 217245863835, 946622690475, 35511547806735, 439116128090640, 5714676453270219435

Offset: 1

Benoit Cloitre, May 31 2002

Cf. A088250, A124516, A124522, A124522, A063983.

Cf. A005097, A123998, A124408-A124411.

k = 1; Do[ While[p = Table[2*i*k + 1, {i, 1, n}]; Union[ PrimeQ[p]] != {True}, k++ ]; Print[k], {n, 1, 15}] (* Robert G. Wilson v *)

for(n=1,6,s=1; while(sum(i=1,n,isprime(2*s*i+1))

Extended by Robert G. Wilson v, Jun 06 2002
a(9) from Ryan Propper, Jun 20 2005
a(10)-a(13) from Don Reble, Nov 05 2006
a(14) from Giovanni Resta, Apr 01 2017

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

Original entry on oeis.org

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

A064215 Least k such that k*6^n +/- 1 are twin primes.

Original entry on oeis.org

1, 2, 2, 2, 18, 3, 33, 255, 212, 115, 147, 102, 17, 33, 308, 87, 198, 33, 172, 418, 210, 35, 158, 847, 1010, 292, 157, 1318, 263, 212, 642, 107, 458, 102, 17, 635, 735, 262, 2422, 3517, 1222, 605, 1362, 227, 367, 602, 207, 2023, 3925, 1857, 822, 137, 5568, 928

Offset: 1

Robert G. Wilson v, Sep 21 2001

nonn

As n increases, a(n) is in average = 0.44*n^2. It appears that 62% of a(n)/n^2 are < 0.44. - Pierre CAMI, Jun 01 2012

R. J. Mathar, Table of n, a(n) for n = 1..240

Cf. A063983.

A064215 := proc(n)
    for k from 1 do
        if isprime(k*6^n-1) and isprime(k*6^n+1) then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Sep 17 2015

Table[ k = 1; While[ ! PrimeQ[ k*6^n + 1 ] || ! PrimeQ[ k*6^n - 1 ], k++ ]; k, {n, 50} ]

A064213 Least k such that k*3^n +- 1 are twin primes.

Original entry on oeis.org

4, 2, 2, 4, 10, 40, 58, 64, 28, 24, 8, 210, 70, 36, 12, 4, 78, 26, 28, 20, 90, 30, 10, 630, 210, 70, 82, 416, 612, 204, 68, 930, 310, 406, 1078, 1164, 388, 176, 190, 334, 190, 726, 242, 1004, 398, 1430, 1372, 2730, 910, 1560, 520

Offset: 0

Robert G. Wilson v, Sep 21 2001

nonn

k must be even because 3^n is odd. - Harry J. Smith, Sep 10 2009

Harry J. Smith, Table of n, a(n) for n = 0..225

Cf. A063983.

Do[ k = 1; While[ ! PrimeQ[ k*3^n + 1 ] || ! PrimeQ[ k*3^n - 1 ], k++ ]; Print[ k ], {n, 0, 50} ]

{ for (n=0, 225, k=0; p=3^n; until (isprime(k*p - 1) && isprime(k*p + 1), k+=2); write("b064213.txt", n, " ", k); ) } \\ Harry J. Smith, Sep 10 2009

Offset changed from 1 to 0 by Harry J. Smith, Sep 10 2009

cp's OEIS Frontend

A125019 Records in A063983 if the initial 4 is ignored (cf. A125848).

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A125848 Records in A063983.

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A045753 Numbers n such that 4n-1 and 4n+1 are both primes.

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A124519 Numbers k such that 12*k - 1 and 12*k + 1 are twin primes.

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A124522 a(n) = smallest k such that 2nk-1 and 2nk+1 are primes.

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Maple

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A071576 a(n) = least k such that 2ik + 1 is prime for all 1 <= i <= n.

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

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Maple

Mathematica

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

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Magma

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Extensions

A064215 Least k such that k*6^n +/- 1 are twin primes.

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A124519 Numbers k such that 12k - 1 and 12k + 1 are twin primes.

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