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.

A161761 Binary representation of A139224(n).

Original entry on oeis.org

11, 10101, 111010001, 1111101000001, 1111111111101000000000001, 111111111111111010000000000000001, 1111111111111111101000000000000000001, 1111111111111111111111111111101000000000000000000000000000001
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 18 2009

Keywords

Crossrefs

Cf. A000396, A000668, A139224, A061652.

Extensions

Keyword:base added by R. J. Mathar, May 21 2010

A139116 a(n) = p*(p-1)/2, where p is A000043(n).

Original entry on oeis.org

1, 3, 10, 21, 78, 136, 171, 465, 1830, 3916, 5671, 8001, 135460, 183921, 817281, 2425503, 2600340, 5172936, 9041878, 9779253, 46933516, 49406770, 62860078, 198732016, 235455850, 269317236, 989969256, 3718884403, 6105401253, 8718403176, 23347552095, 286402257541
Offset: 1

Views

Author

Omar E. Pol, May 10 2008

Keywords

Links

Crossrefs

Cf. A000043, A000217, A036689, A139306, A139307, A139116, A139223, A139224, A139225, A139226.

Programs

  • Mathematica
    (#(#-1))/2&/@MersennePrimeExponent[Range[47]] (* Harvey P. Dale, Aug 13 2021 *)

Formula

a(n) = A000043(n)*(A000043(n)-1)/2.

Extensions

a(24)-a(32) from Harvey P. Dale, Aug 13 2021

A139115 a(n) = p*(p - 1), where p is A000043(n).

Original entry on oeis.org

2, 6, 20, 42, 156, 272, 342, 930, 3660, 7832, 11342, 16002, 270920, 367842, 1634562, 4851006, 5200680, 10345872, 18083756, 19558506, 93867032, 98813540, 125720156, 397464032, 470911700, 538634472, 1979938512, 7437768806, 12210802506
Offset: 1

Views

Author

Omar E. Pol, May 10 2008

Keywords

Links

Crossrefs

Cf. A000043, A036689, A139306, A139307, A139116, A139223, A139224, A139225, A139226.

Programs

  • Mathematica
    #(#-1)&/@MersennePrimeExponent[Range[30]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 15 2020 *)

Formula

a(n) = A000043(n)*(A000043(n) - 1).

Extensions

More terms from Vincenzo Librandi, May 11 2010

A139223 M*(M-1), where M is Mersenne prime A000668(n).

Original entry on oeis.org

6, 42, 930, 16002, 67084290, 17179475970, 274876334082, 4611686011984936962, 5316911983139663484697699213480296450, 383123885216472214589586754930667236976614368197214210
Offset: 1

Views

Author

Omar E. Pol, May 10 2008

Keywords

Links

Crossrefs

Cf. A000668, A036689, A139115, A139116, A139224, A139225, A139226, A139256.

Formula

a(n) = A000668(n)*(A000668(n)-1).

Extensions

More terms from R. J. Mathar, Jun 24 2009

A139225 M(M-1)/3, where M is Mersenne prime A000668(n).

Original entry on oeis.org

2, 14, 310, 5334, 22361430, 5726491990, 91625444694, 1537228670661645654, 1772303994379887828232566404493432150, 127707961738824071529862251643555745658871456065738070, 8776024305713098891493168973639040433964428736682367693182293334, 9649340769776349618630915417390658987602357538676244438223111363610210030934
Offset: 1

Views

Author

Omar E. Pol, May 10 2008

Keywords

Comments

Terms from a(13) on have 314 or more digits and are not listed for that reason. - R. J. Mathar, May 11 2008

Crossrefs

Cf. A000668, A036689, A139115, A139116, A139223, A139224, A139226.

Formula

a(n)=A000668(n)*(A000668(n)-1)/3.

Extensions

More terms from R. J. Mathar, May 11 2008

A139226 M(M-1)/6, where M is Mersenne prime A000668(n).

Original entry on oeis.org

1, 7, 155, 2667, 11180715, 2863245995, 45812722347, 768614335330822827, 886151997189943914116283202246716075, 63853980869412035764931125821777872829435728032869035, 4388012152856549445746584486819520216982214368341183846591146667, 4824670384888174809315457708695329493801178769338122219111555681805105015467
Offset: 1

Views

Author

Omar E. Pol, May 10 2008

Keywords

Comments

Perfect number A000396(n) minus Mersenne prime A000668(n), divided by 3.
Terms from a(13) on have 313 or more digits and are not listed for that reason. - R. J. Mathar, May 11 2008

Links

Crossrefs

Cf. A000217, A000396, A000668, A036689, A139096, A139115, A139116, A139223, A139224, A139225, A139256, A139306.

Formula

a(n) = A000668(n)*(A000668(n)-1)/6 = A139223(n)/6 = A139224(n)/3.
a(n) = (A000396(n)-A000668(n))/3.

Extensions

More terms from R. J. Mathar, May 11 2008

A162385 Alternating sum from the n-th Mersenne prime up to the n-th perfect number.

Original entry on oeis.org

2, 11, 233, 4001, 16771073, 4294868993, 68719083521, 1152921502996234241, 1329227995784915871174424803370074113, 95780971304118053647396688732666809244153592049303553
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jul 21 2009

Keywords

Comments

Define the alternating sum S(k) = sum_{x=0..k} x*(-1)^x = (-1)^k*(k/2+1/4)-1/4 = A130472(k).
a(n) is this sum evaluated with a lower limit of A000668(n) and an upper limit of A000396(n).

Examples

			a(1) = -3+4-5+6 = 2. a(2) = -7+8-9+10-11+12-13+14-15+16-17+...-27+28 = 11.

Crossrefs

Cf. A000396, A000668.

Formula

a(n) = A130472(A000396(n)) - A130472( A000668(n)-1).
a(n) = (A000396(n) - A000668(n) + 1)/2. - César Aguilera, May 13 2017
a(n) = (1 + A139224(n))/2. - Omar E. Pol, May 22 2017

Extensions

Edited and extended by R. J. Mathar, Sep 16 2009
Showing 1-7 of 7 results.

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