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 1-7 of 7 results.

A105652 Numbers k such that p1=2k+3, p2=4k+5 and p3=6k+7 are all prime.

Original entry on oeis.org

0, 2, 17, 104, 134, 152, 164, 167, 299, 362, 584, 617, 647, 764, 827, 1109, 1139, 1277, 1517, 1529, 1532, 2129, 2222, 2399, 2474, 2612, 2789, 2924, 3074, 3179, 3344, 3419, 3482, 3809, 3839, 3842, 3932, 4007, 4082, 4094, 4142, 4259, 4262, 4322, 4469, 4544
Offset: 1

Views

Author

Zak Seidov, Apr 16 2005

Keywords

Comments

Except for 0, all terms == 2 or 14 (mod 15). - Robert Israel, Jun 08 2018

Links

Crossrefs

Cf. A005382, A005383, A105610, A105653 - A105657, A174734.

Programs

  • Magma
    [n: n in [0..5000] | IsPrime(2*n+3) and IsPrime(4*n+5) and IsPrime(6*n+7)]; // Vincenzo Librandi, Nov 13 2010
  • Maple
    select(k -> andmap(isprime, [2*k+3,4*k+5,6*k+7]), [0, seq(seq(15*i+j,j=[2,14]),i=0..1000)]); # Robert Israel, Jun 08 2018

Formula

a(n) = (A174734(n)-3)/2. - Robert Israel, Jun 08 2018

A105657 Numbers n such that p1=2n+3, p2=4n+5, p3=6n+7, p4=8n+9, p5=10n+11, p6=12n+13, p7=14n+15 and p8=16n+17 are all prime.

Original entry on oeis.org

256409, 11120339, 13243229, 49798979, 296504669, 510578774, 520649219, 640598279, 674992499, 713074004, 830453714, 947378984
Offset: 1

Views

Author

Zak Seidov, Apr 16 2005

Keywords

Crossrefs

Cf. A005382, A005383, A105610, A105652 - A105656.

A105653 Numbers n such that p1=2n+3, p2=4n+5, p3=6n+7 and p4=8n+9 are all prime.

Original entry on oeis.org

164, 764, 1529, 2129, 2474, 3419, 5414, 7694, 9059, 11504, 12704, 13019, 15884, 16649, 20054, 20744, 22529, 24914, 26939, 29669, 32924, 35069, 36884, 39269, 44369, 47729, 48464, 54734, 55859, 56309, 58859, 65654, 66599, 67364, 67649
Offset: 1

Views

Author

Zak Seidov, Apr 16 2005

Keywords

Crossrefs

Cf. A005382, A005383, A105610, A105652 - A105657.

A105656 Numbers n such that p1=2n+3, p2=4n+5, p3=6n+7, p4=8n+9, p5=10n+11, p6=12n+13 and p7=14n+15 are all prime.

Original entry on oeis.org

256409, 4112429, 11120339, 12231449, 13243229, 31435739, 46892264, 49798979, 69909839, 98237474, 125994749, 145989164, 171741989, 201038564, 205739414, 229298684, 232560509, 253539929, 259765694, 261519719, 292721519, 296504669
Offset: 1

Views

Author

Zak Seidov, Apr 16 2005

Keywords

Crossrefs

Cf. A005382, A005383, A105610, A105652 - A105657.

Programs

  • Mathematica
    apQ[n_]:=And@@PrimeQ[Table[n*i+i+1,{i,2,14,2}]]; Select[Range[ 300000000],apQ] (* Harvey P. Dale, Jan 02 2013 *)

A105654 Numbers k such that p1=2k+3, p2=4k+5, p3=6k+7, p4=8k+9 and p5=10k+11 are all prime.

Original entry on oeis.org

5414, 12704, 13019, 44369, 82949, 98279, 105524, 112199, 115139, 123854, 134249, 134459, 187739, 188744, 210164, 225704, 247169, 256409, 296309, 302084, 367874, 375644, 382889, 399584, 404039, 476339, 487829, 526844, 532094, 566429, 578084
Offset: 1

Views

Author

Zak Seidov, Apr 16 2005

Keywords

Crossrefs

Cf. A005382, A005383, A105610, A105652..A105657.

Programs

  • Magma
    [n: n in [0..10000000]|IsPrime(2*n+3) and IsPrime(4*n+5) and IsPrime(6*n+7) and IsPrime(8*n+9) and IsPrime(10*n+11)] // Vincenzo Librandi, Dec 16 2010
  • Mathematica
    Select[Range[10^6], Function[n, AllTrue[Array[2 # n + (2 # + 1) &, 5], PrimeQ]]] (* Michael De Vlieger, Jan 20 2018 *)

A105691 Primes p such that both 2p + 3 and 4p + 5 are primes.

Original entry on oeis.org

2, 17, 47, 113, 167, 467, 503, 617, 647, 827, 1013, 1109, 1277, 1307, 1553, 1583, 1847, 2087, 2129, 2309, 2399, 2777, 2789, 3137, 3209, 3767, 3779, 4007, 4157, 4229, 4259, 4523, 4637, 5087, 5297, 5393, 5417, 6257, 6287, 6389, 6719, 6737, 6833, 6863
Offset: 1

Views

Author

Zak Seidov, Apr 17 2005

Keywords

Comments

Primes from A105610.

Links

Crossrefs

Cf. A005382, A005383, A105610.

Programs

  • Magma
    [p: p in PrimesUpTo(7000) |IsPrime(4*p+5) and IsPrime(2*p+3)] // Vincenzo Librandi, Nov 13 2010
  • Mathematica
    Select[Prime@ Range[900], AllTrue[{2 # + 3, 4 # + 5}, PrimeQ] &] (* Michael De Vlieger, Jan 22 2018 *)

A105655 Numbers k such that p1=2k+3, p2=4k+5, p3=6k+7, p4=8k+9, p5=10k+11 and p6=12k+13 are all prime.

Original entry on oeis.org

12704, 13019, 105524, 256409, 966839, 1707509, 1944494, 2309999, 2478629, 3132674, 3836069, 3976769, 4112429, 4532324, 5499584, 5920004, 6610484, 7390844, 8552249, 10739504, 11120339, 12231449, 12338129, 13243229, 16467254
Offset: 1

Views

Author

Zak Seidov, Apr 16 2005

Keywords

Crossrefs

Cf. A005382, A005383, A105610, A105652, A105653, A105654, A105656, A105657.

Programs

  • Magma
    [n: n in [0..10000000]|IsPrime(2*n+3) and IsPrime(4*n+5) and IsPrime(6*n+7) and IsPrime(8*n+9) and IsPrime(10*n+11)and IsPrime(12*n+13)] // Vincenzo Librandi, Dec 16 2010
  • Mathematica
    With[{r1=Range[2,12,2],r2=Range[3,13,2]},Select[Range[16500000],And@@PrimeQ[# r1+r2]&]] (* Harvey P. Dale, Jan 31 2011 *)
Showing 1-7 of 7 results.

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