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 25 results. Next

A067026 (Prime(n)# - 4)/2 is prime, where x# is the primorial A034386(x).

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 11, 13, 16, 20, 27, 39, 83, 103, 122, 129, 145, 279, 393, 608, 798, 929, 1164, 1266, 1491, 2043, 3276, 3426, 7119, 15711, 18424
Offset: 1

Views

Author

Labos Elemer, Dec 29 2001

Keywords

Comments

n such that A002110(n)/2 - 2 is prime.
a(33) > 25000. - Robert Price, Sep 29 2017

Crossrefs

Cf. A002110, A067024, A067027.

Programs

  • Mathematica
    p = 1; Do[p = p*Prime[n]; If[PrimeQ[(p - 4)/2], Print[n]], {n, 1, 400} ]
Flatten[Position[Rest[FoldList[Times,1,Prime[Range[2100]]]],?(PrimeQ[(#-4)/2]&)]] (* _Harvey P. Dale, Nov 22 2014 *)

Extensions

More terms from Robert G. Wilson v, Dec 30 2001
a(21)-a(27) from Ray Chandler, Jun 16 2013
a(28)-a(32) from Robert Price, Sep 29 2017

A103514 a(n) is the smallest m such that primorial(n)/2 - 2^m is prime.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 25, 2, 1, 6, 6, 19, 1, 13, 3, 3, 11, 29, 2, 1, 6, 3, 4, 2, 6, 4, 15, 6, 4, 20, 4, 1, 7, 16, 4, 7, 22, 3, 12, 13, 9, 35, 2, 3, 3, 52, 35, 3, 32, 15, 13, 10, 53, 56, 9, 16, 36, 5, 8, 5, 22, 3, 14, 2, 64, 37, 8, 22, 42, 11, 22, 22, 12, 11, 26, 1, 54, 187, 20, 9
Offset: 2

Views

Author

Lei Zhou, Feb 15 2005

Keywords

Examples

			P(2)/2-2^0=2 is prime, so a(2)=0;
P(10)/2-2^3=3234846607 is Prime, so a(10)=3.

Links

Crossrefs

Cf. A002110, A005234, A014545, A018239, A006794, A057704, A057705, A103153, A067026, A067027, A139439, A139440, A139441, A139442, A139443, A139444, A139445, A139446, A139447, A139448, A139449, A139450, A139451, A139452, A139453, A139454, A139455, A139456, A139457, A103514.

Programs

  • Mathematica
    nmax = 2^8192; npd = 1; n = 2; npd = npd*Prime[n]; While[npd < nmax, tn = 1; tt = 2; cp = npd - tt; While[(cp > 1) && (! (PrimeQ[cp])), tn = tn + 1; tt = tt*2; cp = npd - tt]; If[cp < 2, Print["*"], Print[tn]]; n = n + 1; npd = npd*Prime[n]]
(* Second program: *)
k = 1; a = {}; Do[k = k*Prime[n]; m = 1; While[ ! PrimeQ[k - 2^m], m++ ]; Print[m]; AppendTo[a, m], {n, 2, 200}]; a (* Artur Jasinski, Apr 21 2008 *)
  • PARI
    a(n)=my(t=prod(i=2,n,prime(i)),m); while(!isprime(t-2^m),m++); m \\ Charles R Greathouse IV, Apr 28 2015

Extensions

Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar

A139439 Numbers n such that primorial(n)/2 + 4 is prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 18, 21, 70, 76, 323, 340, 556, 572, 3433, 5457, 5897, 10820
Offset: 1

Views

Author

Artur Jasinski, Apr 21 2008

Keywords

Comments

a(17) > 25000. - Robert Price, Nov 11 2016

Crossrefs

Cf. A067026, A067027, A139439-A139457, A103514.

Programs

Extensions

a(1)=1 inserted and a(12)-a(13) from Ray Chandler, Jun 16 2013
a(14)-a(16) from Robert Price, Nov 11 2016

A139457 a(n)= smallest m such that primorial(n)/2 + 2^m is prime.

Original entry on oeis.org

0, 1, 1, 1, 3, 1, 2, 4, 3, 1, 1, 1, 4, 10, 1, 11, 1, 2, 11, 14, 2, 8, 7, 3, 4, 4, 26, 21, 1, 4, 15, 10, 8, 4, 16, 29, 10, 3, 51, 17, 5, 12, 12, 48, 13, 45, 12, 1, 20, 17, 65, 12, 8, 95, 5, 12, 11, 8, 110, 38, 28, 8, 1, 23, 13, 5, 7, 11, 21, 2, 20, 32, 9, 66, 4, 2, 1, 20, 34, 97, 28, 80
Offset: 1

Views

Author

Artur Jasinski, Apr 21 2008

Keywords

Crossrefs

Cf. A067026, A067027, A139439-A139457, A103514.

Programs

  • Mathematica
    k = 1/2; a = {}; Do[k = k*Prime[n]; m = 0; While[ ! PrimeQ[k + 2^m], m++ ]; Print[m]; AppendTo[a, m], {n, 100}]; a
  • PARI
    a(n)=my(t=prod(i=2,n,prime(i)),m); while(!isprime(t+2^m), m++); m \\ Charles R Greathouse IV, Apr 28 2015

Extensions

a(1)=0 inserted and program corrected by Ray Chandler, Jun 16 2013

A139441 Numbers n such that primorial(n)/2 + 8 is prime.

Original entry on oeis.org

2, 3, 4, 5, 9, 11, 12, 18, 24, 29, 38, 76, 146, 152, 187, 200, 404, 442, 504, 950, 2796, 5133, 5683, 11334, 13775, 20539, 21253
Offset: 1

Views

Author

Artur Jasinski, Apr 21 2008

Keywords

Comments

a(28) > 25000. - Robert Price, Jan 01 2017

Crossrefs

Cf. A067026, A067027, A139439-A139457, A103514.

Programs

  • Mathematica
    k = 1/2; a = {}; Do[k = k*Prime[n]; If[PrimeQ[k + 8], Print[n]; AppendTo[a, n]], {n, 404}]; a
(* Second program *)
Select[Range[10^3], PrimeQ[(Times @@ Prime@ Range@ #)/2 + 8] &] (* Michael De Vlieger, Jan 01 2017 *)

Extensions

a(18)-a(21) from Ray Chandler, Jun 16 2013
a(22)-a(27) from Robert Price, Jan 01 2017

A139440 Numbers n such that primorial(n)/2 - 4 is prime.

Original entry on oeis.org

3, 4, 5, 7, 12, 15, 26, 31, 50, 71, 186, 273, 366, 1542, 1929, 3687, 4407, 15395, 15433
Offset: 1

Views

Author

Artur Jasinski, Apr 21 2008

Keywords

Comments

a(20) > 25000. - Robert Price, Dec 03 2016

Crossrefs

Cf. A067026, A067027, A139439-A139457, A103514.

Programs

  • Mathematica
    k = 1; a = {}; Do[k = k*Prime[n]; If[PrimeQ[k - 4], Print[n]; AppendTo[a, n]], {n, 2, 366}]; a

Extensions

a(14)-a(15) from Ray Chandler, Jun 16 2013
a(16)-a(17) from Robert Price, Aug 16 2016
a(18) from Robert Price, Dec 03 2016
Added missing term, 15395 by Robert Price, Dec 28 2016

A139442 Numbers n such that primorial(n)/2 - 8 is prime.

Original entry on oeis.org

3, 4, 7, 9, 10, 11, 13, 15, 22, 23, 29, 45, 51, 52, 55, 69, 98, 122, 157, 268, 367, 476, 481, 1670, 1964, 2736, 4696, 7933, 22245
Offset: 1

Views

Author

Artur Jasinski, Apr 21 2008

Keywords

Comments

a(30) > 25000. - Robert Price, Jan 13 2017

Crossrefs

Cf. A067026, A067027, A139439-A139457, A103514.

Programs

  • Mathematica
    k = 1; a = {}; Do[k = k*Prime[n]; If[PrimeQ[k - 8] && k > 8, Print[n]; AppendTo[a, n]], {n, 2, 481}]; a
  • PARI
    is(n)=ispseudoprime(prod(i=2,n,prime(i))-8) \\ Charles R Greathouse IV, Jun 13 2013

Extensions

a(24)-a(25) from Charles R Greathouse IV, Jun 13 2013
a(26)-a(27) from Ray Chandler, Jun 16 2013
a(28)-a(29) from Robert Price, Jan 13 2017

A139443 Numbers n such that primorial(n)/2 + 16 is prime.

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 13, 25, 26, 30, 34, 63, 75, 138, 149, 672, 752, 1067, 1256, 1370, 3357, 4120, 6672, 7201, 7469, 8738, 9426, 11608
Offset: 1

Views

Author

Artur Jasinski, Apr 21 2008

Keywords

Comments

a(29) > 25000. - Robert Price, Dec 08 2016

Crossrefs

Cf. A067026, A067027, A139439-A139457, A103514.

Programs

  • Mathematica
    k = 1/2; a = {}; Do[k = k*Prime[n]; If[PrimeQ[k + 16], Print[n]; AppendTo[a, n]], {n, 752}]; a

Extensions

a(1)=1 inserted and program corrected, a(18)-a(20) from Ray Chandler, Jun 16 2013
a(21)-a(28) from Robert Price, Dec 08 2016

A139444 Numbers n such that primorial(n)/2 - 16 is prime.

Original entry on oeis.org

4, 7, 9, 13, 22, 26, 30, 33, 36, 38, 42, 114, 125, 126, 181, 291, 296, 386, 1415, 2573, 3727, 5574, 7523, 8682, 9765
Offset: 1

Views

Author

Artur Jasinski, Apr 21 2008

Keywords

Comments

a(26) > 25000. - Robert Price, Feb 25 2017

Crossrefs

Cf. A067026, A067027, A139439-A139457, A103514.

Programs

  • Mathematica
    k = 1; a = {}; Do[k = k*Prime[n]; If[PrimeQ[k - 16] && k>16, Print[n]; AppendTo[a, n]], {n, 2, 752}]; a

Extensions

Drop 2 and correct program, a(16)-a(20) from Ray Chandler, Jun 16 2013
a(21)-a(25) from Robert Price, Feb 25 2017

A139445 Numbers n such that primorial(n)/2 + 32 is prime.

Original entry on oeis.org

3, 4, 5, 10, 11, 13, 41, 55, 66, 94, 104, 325, 363, 424, 672, 734, 818, 1044, 1389, 1595, 1728, 2870, 3149, 3922, 5352, 9431, 11586, 13991, 17507
Offset: 1

Views

Author

Artur Jasinski, Apr 21 2008

Keywords

Comments

a(30)>25000. - Robert Price, Dec 28 2016

Crossrefs

Cf. A067026, A067027, A139439-A139457, A103514.

Programs

Extensions

a(13)-a(22) from Ray Chandler, Jun 16 2013
a(23)-a(29) from Robert Price, Dec 28 2016
Showing 1-10 of 25 results. Next

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

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