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 1-9 of 9 results.

A139286 a(n) = 2^(2*prime(n) - 1).

Original entry on oeis.org

8, 32, 512, 8192, 2097152, 33554432, 8589934592, 137438953472, 35184372088832, 144115188075855872, 2305843009213693952, 9444732965739290427392, 2417851639229258349412352, 38685626227668133590597632, 9903520314283042199192993792
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A000040, A000079, A076274, A139287, A139288, A139289, A139290, A139291, A139292, A139293, A139294, A139306.

Programs

Extensions

Corrected and extended by Harvey P. Dale, Dec 01 2017

A139290 2^(2p - 1)/4, where p is prime.

Original entry on oeis.org

2, 8, 128, 2048, 524288, 8388608, 2147483648, 34359738368, 8796093022208, 36028797018963968, 576460752303423488, 2361183241434822606848, 604462909807314587353088, 9671406556917033397649408
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A139286, A139287, A139288, A139289, A139290, A139292, A139293, A139294, A139306.

Programs

  • Magma
    [2^(2*p-1)div 4: p in PrimesUpTo(200)]; // Vincenzo Librandi, Dec 15 2010
  • Mathematica
    2^(2#-1)/4 & /@ Prime@ Range@ 15 (* Harvey P. Dale, Dec 16 2010 *)

Formula

a(n) = A139286(n)/4.

Extensions

More terms from Jon E. Schoenfield, Jul 16 2010

A139288 2^(2p - 1)/2, where p is prime.

Original entry on oeis.org

4, 16, 256, 4096, 1048576, 16777216, 4294967296, 68719476736, 17592186044416, 72057594037927936, 1152921504606846976, 4722366482869645213696, 1208925819614629174706176, 19342813113834066795298816
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A139286, A139287, A139289, A139290, A139291, A139292, A139293, A139294, A139306.

Programs

  • Mathematica
    Table[2^(2p-1)/2,{p,Prime[Range[20]]}] (* Harvey P. Dale, Jun 21 2021 *)

Formula

a(n)=A139286(n)/2.

Extensions

More terms from Jon E. Schoenfield, Jul 16 2010

A139289 (2^(2p - 1)/2)-1, where p is prime.

Original entry on oeis.org

3, 15, 255, 4095, 1048575, 16777215, 4294967295, 68719476735, 17592186044415, 72057594037927935, 1152921504606846975, 4722366482869645213695, 1208925819614629174706175, 19342813113834066795298815, 4951760157141521099596496895, 20282409603651670423947251286015, 83076749736557242056487941267521535
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Links

Crossrefs

Cf. A139286, A139287, A139288, A139290, A139291, A139292, A139293, A139294, A139306.

Programs

  • Mathematica
    Table[(2^(2 Prime[p] - 1)/2) - 1, {p, 1, 20}] (* Floris P. van Doorn and Jasper Mulder (florisvandoorn(AT)hotmail.com), Oct 12 2009 *)

Formula

a(n) = A139286(n)/2 - 1.

Extensions

More terms from Floris P. van Doorn and Jasper Mulder (florisvandoorn(AT)hotmail.com), Oct 12 2009

A139292 2^(2p - 1)/8, where p is prime.

Original entry on oeis.org

1, 4, 64, 1024, 262144, 4194304, 1073741824, 17179869184, 4398046511104, 18014398509481984, 288230376151711744, 1180591620717411303424, 302231454903657293676544, 4835703278458516698824704
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A139286, A139287, A139288, A139289, A139290, A139291, A139293, A139294, A139306.

Programs

  • Mathematica
    2^(2#-1)/8&/@Prime[Range[20]] (* Harvey P. Dale, Aug 19 2012 *)

Formula

a(n) = A139286(n)/8.

Extensions

More terms from Jon E. Schoenfield, Jul 16 2010

A139293 (2^(2p - 1)/8)-1, where p is prime.

Original entry on oeis.org

0, 3, 63, 1023, 262143, 4194303, 1073741823, 17179869183, 4398046511103, 18014398509481983, 288230376151711743, 1180591620717411303423, 302231454903657293676543, 4835703278458516698824703
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A139286, A139287, A139288, A139289, A139290, A139291, A139292, A139294, A139306.

Programs

  • Mathematica
    (2^(2#-1))/8-1&/@Prime[Range[30]] (* Harvey P. Dale, May 09 2012 *)

Formula

a(n) = (A139286(n)/8)-1.

Extensions

More terms from Jon E. Schoenfield, Jul 16 2010

A139291 a(n) = 2^(2*prime(n) - 3) - 1.

Original entry on oeis.org

1, 7, 127, 2047, 524287, 8388607, 2147483647, 34359738367, 8796093022207, 36028797018963967, 576460752303423487, 2361183241434822606847, 604462909807314587353087, 9671406556917033397649407, 2475880078570760549798248447, 10141204801825835211973625643007
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A139286, A139287, A139288, A139289, A139290, A139293, A139294, A139306.

Programs

  • Mathematica
    (2^(2#-1))/4-1&/@Prime[Range[20]] (* Harvey P. Dale, May 08 2011 *)

Formula

a(n) = A139286(n)/4 - 1.
a(n) = A000225(A131426(n)). - Max Alekseyev, Mar 07 2020
a(n) = A139290(n) - 1. - Omar E. Pol, Mar 10 2020

Extensions

Edited by Max Alekseyev, May 03 2009, Mar 07 2020

A139307 a(n) = (2^(2*p - 1)) - 1, where p is A000043(n).

Original entry on oeis.org

7, 31, 511, 8191, 33554431, 8589934591, 137438953471, 2305843009213693951, 2658455991569831745807614120560689151, 191561942608236107294793378393788647952342390272950271
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008, May 08 2008

Keywords

Comments

Ultraperfect numbers (A139306) minus 1.

Examples

			a(5) = 33554431 because A000043(5) = 13 and (2^(2*13 - 1))-1 = 2^25 - 1 = 33554431.

Links

Crossrefs

Cf. A000043, A139287, A139295, A139306.

Programs

  • Mathematica
    2^(2 * MersennePrimeExponent[Range[10]] - 1) - 1 (* Amiram Eldar, Oct 17 2024 *)

Formula

a(n) = (2^(2*A000043(n) - 1)) - 1 = A139306(n) - 1.

A139314 Primes of the form 2^(2p - 1) - 1, where p is prime.

Original entry on oeis.org

7, 31, 8191, 2305843009213693951
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Comments

Primes in A139287.
This sequence is a subsequence of A000668. From A000043, a(5) = 2^3217 - 1.
The next term a(6) is an unknown Mersenne prime. [Washington Bomfim, Nov 18 2009]
a(5) has 969 digits. - Vincenzo Librandi, Dec 14 2010
The first three terms can be written as (n^3 - 1)/(n - 1) for some n. [Arkadiusz Wesolowski, May 09 2012]

Links

Crossrefs

Cf. A139286, A139287.
Cf. A000668, A000043. [Washington Bomfim, Nov 18 2009]

Programs

  • Magma
    [a: p in PrimesUpTo(4200) | IsPrime(a) where a is 2^(2*p-1)-1]; // Vincenzo Librandi, Dec 14 2010
Showing 1-9 of 9 results.

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