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 1-8 of 8 results.

A128122 Numbers m such that 2^m == 6 (mod m).

Original entry on oeis.org

1, 2, 10669, 6611474, 43070220513807782
Offset: 1

Views

Author

Alexander Adamchuk, Feb 15 2007

Keywords

Comments

No other terms below 10^17. - Max Alekseyev, Nov 18 2022
A large term: 862*(2^861-3)/281437921287063162726198552345362315020202285185118249390789 (203 digits). - Max Alekseyev, Sep 24 2016

Examples

			2 == 6 (mod 1), so 1 is a term;
4 == 6 (mod 2), so 2 is a term.

Links

Crossrefs

Solutions to 2^m == k (mod m): A000079 (k=0),A187787 (k=1/2), A296369 (k=-1/2), A006521 (k=-1), A296370 (k=3/2), A015919 (k=2), A006517 (k=-2), A050259 (k=3), A015940 (k=-3), A015921 (k=4), A244673 (k=-4), A128121 (k=5), A245318 (k=-5), this sequence (k=6), A245728 (k=-6), A033981 (k=7), A240941 (k=-7), A015922 (k=8), A245319 (k=-8), A051447 (k=9), A240942 (k=-9), A128123 (k=10), A245594 (k=-10), A033982 (k=11), A128124 (k=12), A051446 (k=13), A128125 (k=14), A033983 (k=15), A015924 (k=16), A124974 (k=17), A128126 (k=18), A125000 (k=19), A015925 (k=2^5), A015926 (k=2^6), A015927 (k=2^7), A015929 (k=2^8), A015931 (k=2^9), A015932 (k=2^10), A015935 (k=2^11), A015937 (k=2^12)
Cf. A015910, A036236.

Programs

  • Mathematica
    m = 6; Join[Select[Range[m], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^6], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 08 2018 *)

Extensions

1 and 2 added by N. J. A. Sloane, Apr 23 2007
a(5) from Max Alekseyev, Nov 18 2022

A215611 Odd integers n such that 2^n == 2^8 (mod n).

Original entry on oeis.org

1, 127, 3473, 19313, 30353, 226703, 230777, 345023, 929783, 1790159, 1878073, 2569337, 3441743, 4213511, 8026103, 9770153, 19139183, 24261623, 30652223, 35482433, 38044223, 40642103, 55015793, 65046479, 67411121, 69601193, 119611073
Offset: 1

Views

Author

Max Alekseyev, Aug 17 2012

Keywords

Comments

Also, the odd solutions to 2^(n-8) == 1 (mod n). The only even solution is n=8.
For all m, 2^A051447(m)-1 belongs to this sequence.

Links

Crossrefs

The odd terms of A015929.
Cf. A051447, A033984, A173572, A215610, A215612, A215613.

Programs

  • Mathematica
    m = 2^8; Join[Select[Range[1, m, 2], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^6, 2], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 12 2018 *)

A296369 Numbers m such that 2^m == -1/2 (mod m).

Original entry on oeis.org

1, 5, 65, 377, 1189, 1469, 25805, 58589, 134945, 137345, 170585, 272609, 285389, 420209, 538733, 592409, 618449, 680705, 778805, 1163065, 1520441, 1700945, 2099201, 2831009, 4020029, 4174169, 4516109, 5059889, 5215769
Offset: 1

Views

Author

Max Alekseyev, Dec 10 2017

Keywords

Comments

Equivalently, 2^(m+1) == -1 (mod m), or m divides 2^(m+1) + 1.
The sequence is infinite, see A055685.

Links

Crossrefs

Solutions to 2^m == k (mod m): A296370 (k=3/2), A187787 (k=1/2), this sequence (k=-1/2), A000079 (k=0), A006521 (k=-1), A015919 (k=2), A006517 (k=-2), A050259 (k=3), A015940 (k=-3), A015921 (k=4), A244673 (k=-4), A128121 (k=5), A245318 (k=-5), A128122 (k=6), A245728 (k=-6), A033981 (k=7), A240941 (k=-7), A015922 (k=8), A245319 (k=-8), A051447 (k=9), A240942 (k=-9), A128123 (k=10), A245594 (k=-10), A033982 (k=11), A128124 (k=12), A051446 (k=13), A128125 (k=14), A033983 (k=15), A015924 (k=16), A124974 (k=17), A128126 (k=18), A125000 (k=19), A015925 (k=2^5), A015926 (k=2^6), A015927 (k=2^7), A015929 (k=2^8), A015931 (k=2^9), A015932 (k=2^10), A015935 (k=2^11), A015937 (k=2^12)

Programs

  • Mathematica
    Select[Range[10^5], Divisible[2^(# + 1) + 1, #] &] (* Robert Price, Oct 11 2018 *)
  • Python
    A296369_list = [n for n in range(1,10**6) if pow(2,n+1,n) == n-1] # Chai Wah Wu, Nov 04 2019

Formula

a(n) = A055685(n) - 1.

Extensions

Incorrect term 4285389 removed by Chai Wah Wu, Nov 04 2019

A015926 Positive integers n such that 2^n == 2^6 (mod n).

Original entry on oeis.org

1, 2, 4, 6, 8, 10, 12, 16, 18, 24, 30, 31, 32, 36, 42, 48, 64, 66, 72, 78, 84, 90, 96, 102, 114, 126, 138, 144, 168, 174, 176, 186, 192, 210, 222, 234, 246, 252, 258, 282, 288, 318, 336, 354, 366, 390, 396, 402, 426, 438, 456, 474, 496, 498, 504, 510, 534, 546
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Comments

The odd terms are given by A215610.
For all m, 2^A033981(m)-1 belongs to this sequence.

Links

Crossrefs

Contains A208154 as a subsequence.
Cf. A015919, A015921, A015922, A015924, A015925, A015927, A015929, A015931, A015932, A015935, A015937.

Programs

  • Mathematica
    Select[Range[1000], Mod[2^# - 2^6, #] == 0 &] (* T. D. Noe, Aug 17 2012 *)

Extensions

Edited by Max Alekseyev, Jul 30 2011

A015932 Positive integers n such that 2^n == 2^10 (mod n).

Original entry on oeis.org

1, 2, 4, 6, 7, 8, 10, 12, 16, 24, 28, 30, 32, 34, 48, 50, 64, 70, 73, 96, 110, 112, 128, 130, 150, 170, 190, 192, 230, 256, 290, 310, 330, 370, 384, 410, 430, 442, 448, 470, 512, 530, 532, 550, 590, 610, 670, 710
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Comments

The odd terms are given by A215612.
For all m, 2^A033982(m)-1 belongs to this sequence.

Links

Crossrefs

Contains A208158 as a subsequence.
Cf. A015919, A015921, A015922, A015924, A015925, A015926, A015927, A015929, A015931, A015935, A015937.

Programs

  • Mathematica
    Select[Range[1000], Mod[2^# - 2^10, #] == 0 &] (* T. D. Noe, Aug 17 2012 *)

Extensions

Edited by Max Alekseyev, Jul 30 2011

A015937 Positive integers n such that 2^n == 2^12 (mod n).

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 16, 18, 20, 22, 23, 24, 32, 36, 40, 42, 48, 60, 62, 64, 68, 72, 80, 84, 89, 96, 120, 126, 128, 132, 144, 156, 160, 168, 180, 192, 204, 228, 240, 252, 256, 276, 288, 312, 320, 336, 340, 348, 352, 360, 372, 384, 420, 444, 462
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Comments

The odd terms are given by A215613.
For all m, 2^A051446(m)-1 belongs to this sequence.

Links

Crossrefs

Cf. A015919, A015921, A015922, A015924, A015925, A015926, A015927, A015929, A015931, A015932, A015935.

Programs

  • Mathematica
    With[{c=2^12},Select[Range[1,6000],Divisible[2^#-c,#]&]] (* Harvey P. Dale, Mar 20 2011 *)

Extensions

Edited by Max Alekseyev, Jul 31 2011

A296370 Numbers m such that 2^m == 3/2 (mod m).

Original entry on oeis.org

1, 111481, 465793, 79036177, 1781269903307, 250369632905747, 708229497085909, 15673900819204067
Offset: 1

Views

Author

Max Alekseyev, Dec 11 2017

Keywords

Comments

Equivalently, 2^(m+1) == 3 (mod m).
Also, numbers m such that 2^(m+1) - 2 is a Fermat pseudoprime base 2, i.e., 2^(m+1) - 2 belongs to A015919 and A006935.
Some larger terms (may be not in order): 2338990834231272653581, 341569682872976768698011746141903924998969680637.

Links

Crossrefs

Solutions to 2^m == k (mod m): this sequence (k=3/2), A187787 (k=1/2), A296369 (k=-1/2), A000079 (k=0), A006521 (k=-1), A015919 (k=2), A006517 (k=-2), A050259 (k=3), A015940 (k=-3), A015921 (k=4), A244673 (k=-4), A128121 (k=5), A245318 (k=-5), A128122 (k=6), A245728 (k=-6), A033981 (k=7), A240941 (k=-7), A015922 (k=8), A245319 (k=-8), A051447 (k=9), A240942 (k=-9), A128123 (k=10), A245594 (k=-10), A033982 (k=11), A128124 (k=12), A051446 (k=13), A128125 (k=14), A033983 (k=15), A015924 (k=16), A124974 (k=17), A128126 (k=18), A125000 (k=19), A015925 (k=2^5), A015926 (k=2^6), A015927 (k=2^7), A015929 (k=2^8), A015931 (k=2^9), A015932 (k=2^10), A015935 (k=2^11), A015937 (k=2^12)

Programs

  • Mathematica
    Select[Range[10^6], Divisible[2^(# + 1) - 3, #] &] (* Robert Price, Oct 11 2018 *)

Formula

a(n) = A296104(n) - 1.

A334634 Numbers m that divide 2^m + 11.

Original entry on oeis.org

1, 13, 16043199041, 91118493923, 28047837698634913
Offset: 1

Views

Author

Max Alekseyev, Sep 10 2020

Keywords

Comments

Equivalently, numbers m such that 2^m == -11 (mod m).
No other terms below 10^17.

Links

Crossrefs

Solutions to 2^n == k (mod n): A296370 (k=3/2), A187787 (k=1/2), A296369 (k=-1/2), A000079 (k=0), A006521 (k=-1), A015919 (k=2), A006517 (k=-2), A050259 (k=3), A015940 (k=-3), A015921 (k=4), A244673 (k=-4), A128121 (k=5), A245318 (k=-5), A128122 (k=6), A245728 (k=-6), A033981 (k=7), A240941 (k=-7), A015922 (k=8), A245319 (k=-8), A051447 (k=9), A240942 (k=-9), A128123 (k=10), A245594 (k=-10), A033982 (k=11), this sequence (k=-11), A128124 (k=12), A051446 (k=13), A128125 (k=14), A033983 (k=15), A015924 (k=16), A124974 (k=17), A128126 (k=18), A125000 (k=19), A015925 (k=2^5), A015926 (k=2^6), A015927 (k=2^7), A015929 (k=2^8), A015931 (k=2^9), A015932 (k=2^10), A015935 (k=2^11), A015937 (k=2^12).

Extensions

a(5) from Sergey Paramonov, Oct 10 2021
Showing 1-8 of 8 results.

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

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