cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 12 results. Next

A124742 Records in A124522.

Original entry on oeis.org

2, 9, 12, 15, 48, 60, 129, 150, 198, 234, 273, 285, 297, 372, 420, 531, 537, 900, 1065, 1086, 1128, 1746, 1896, 2187, 2229, 2244, 2289, 2415, 2424, 2577, 2781, 2877, 3108, 3126, 3630
Offset: 1

Views

Author

Klaus Brockhaus, Nov 07 2006

Keywords

Crossrefs

Cf. A124522, A124743 (where records occur).

Programs

  • Mathematica
    skp[n_]:=Module[{k=1},While[AnyTrue[2n k+{1,-1},CompositeQ],k++];k]; DeleteDuplicates[ Join[{2},Array[skp,10^6,2]],GreaterEqual] (* The program generates the first 23 terms of the sequence. *) (* Harvey P. Dale, Mar 30 2024 *)

A124743 Where records occur in A124522.

Original entry on oeis.org

1, 4, 8, 14, 28, 53, 61, 382, 433, 584, 1732, 1858, 2047, 2603, 4079, 8546, 9967, 10789, 76943, 81439, 121763, 139736, 626939, 1787252, 3334846, 3585509, 3810949, 3988066, 8407129, 8891182, 9299471, 19279903, 19498462, 36426301, 38235389
Offset: 1

Views

Author

Klaus Brockhaus, Nov 07 2006

Keywords

Crossrefs

Cf. A124522, A124742 (records).

A063983 Least k such that k*2^n +/- 1 are twin primes.

Original entry on oeis.org

4, 2, 1, 9, 12, 6, 3, 9, 57, 30, 15, 99, 165, 90, 45, 24, 12, 6, 3, 69, 132, 66, 33, 486, 243, 324, 162, 81, 90, 45, 345, 681, 585, 375, 267, 426, 213, 429, 288, 144, 72, 36, 18, 9, 147, 810, 405, 354, 177, 1854, 927, 1125, 1197, 666, 333, 519, 1032, 516, 258, 129, 72
Offset: 0

Views

Author

Robert G. Wilson v, Sep 06 2001

Keywords

Comments

Excluding the first three terms, all remaining terms have digital root 3, 6, or 9. - J. W. Helkenberg, Jul 24 2013

Examples

			a(3) = 9 because 9*2^3 = 72 and 71 and 73 are twin primes.
a(6) = 3 because 3*2^6 = 192 and {191, 193} are twin primes.
a(71) = 630 because 630*2^71 = 1487545442103938242314240 and {1487545442103938242314239, 1487545442103938242314241} are twin primes.

References

  • Richard Crandall and Carl Pomerance, 'Prime Numbers: A Computational Perspective,' Springer-Verlag, NY, 2001, page 12.

Links

Crossrefs

Cf. A040040, A045753, A002822, A124065, A124518-A124522.
Cf. A071256, A060210, A060256. For records see A125848, A125019.
Cf. A076806 (requires odd k).

Programs

  • Mathematica
    Table[Do[s=(2^j)*k; If[PrimeQ[s-1]&&PrimeQ[s+1],Print[{j,k}]], {k,1,2*j^2}],{j,0,100}]; (* outprint of a[j]=k *)
Do[ k = 1; While[ ! PrimeQ[ k*2^n + 1 ] || ! PrimeQ[ k*2^n - 1 ], k++ ]; Print[ k ], {n, 0, 50} ]
f[n_] := Block[{k = 1},While[Nand @@ PrimeQ[{-1, 1} + 2^n*k], k++ ];k];Table[f[n], {n, 0, 60}] (* Ray Chandler, Jan 09 2009 *)

Extensions

More terms from Labos Elemer, May 24 2002
Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar

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

Original entry on oeis.org

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

Views

Author

Felice Russo

Keywords

Examples

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

Links

Crossrefs

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

Programs

  • Magma
    [n: n in [1..2000] | IsPrime(4*n+1) and IsPrime(4*n-1)] // Vincenzo Librandi, Nov 18 2010
  • Mathematica
    Select[Range[1023], And @@ PrimeQ[{-1, 1} + 4# ] &] (* Ray Chandler, Dec 06 2006 *)
  • PARI
    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

Extensions

More terms from Erich Friedman

A124519 Numbers k such that 12*k - 1 and 12*k + 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

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Examples

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

Links

Crossrefs

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

Programs

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

Extensions

Extended by Ray Chandler, Nov 16 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

Views

Author

Benoit Cloitre, May 31 2002

Keywords

Crossrefs

Cf. A088250, A124516, A124522, A124522, A063983.
Cf. A005097, A123998, A124408-A124411.

Programs

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

Extensions

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

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Comments

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

Links

Crossrefs

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

Programs

  • Maple
    select(t -> isprime(10*t+1) and isprime(10*t-1), [seq(i,i=3..1000,3)]); # Robert Israel, Apr 07 2019
  • Mathematica
    Select[Range[678], And @@ PrimeQ[{-1, 1} + 10# ] &] (* Ray Chandler, Nov 16 2006 *)

A124065 Numbers k such that 8*k - 1 and 8*k + 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

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Examples

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

Links

Crossrefs

Intersection of A005122 and A005123.
Cf. A040040, A045753, A002822, A124518, A124519, A124520, A124521, A124522, A063983.

Programs

  • Magma
    [n: n in [1..2000] | IsPrime(8*n+1) and IsPrime(8*n-1)] // Vincenzo Librandi, Mar 08 2010
  • Mathematica
    Select[Range[1500], And @@ PrimeQ[{-1, 1} + 8# ] &] (* Ray Chandler, Nov 16 2006 *)
  • Python
    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

Extensions

Extended by Ray Chandler, Nov 16 2006

A124520 Numbers k such that 14*k - 1 and 14*k + 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

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Examples

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

Links

Crossrefs

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

Programs

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

Extensions

Extended by Ray Chandler, Nov 16 2006

A124521 Numbers k such that 16*k - 1 and 16*k + 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

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Examples

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

Links

Crossrefs

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

Programs

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

Extensions

Extended by Ray Chandler, Nov 16 2006
Showing 1-10 of 12 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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