A033982 -id:A033982 - cp's OEIS frontend

A033983 Integers n such that 2^n == 15 (mod n).

Original entry on oeis.org

1, 13, 481, 44669, 1237231339, 1546675117, 62823773963, 284876771881, 1119485807557, 26598440989093

Offset: 1

Joe K. Crump (joecr(AT)carolina.rr.com)

No other terms below 10^14.

Joe K. Crump, 2^n mod n
OEIS Wiki, 2^n mod n

Cf. A125000, A124974, A033982, A033981, A050259, A124977, A124965, A015911, A015910.

Cf. A015910, A015911, A033981, A050259, A124965, A124974, A124977, A015910, A015911, A033982, A125000.

m = 15; Join[Select[Range[m], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^3], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 08 2018 *)

One more term from Joe K. Crump (joecr(AT)carolina.rr.com), Jun 20 2000
Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar
Terms 1, 13 prepended by Max Alekseyev, May 18 2011
a(10) from Max Alekseyev, Dec 15 2013

A051447 Integers n such that 2^n == 9 (mod n).

Original entry on oeis.org

1, 7, 2228071, 16888457, 352978207, 1737848873, 77362855777, 567442642711

Offset: 1

Joe K. Crump (joecr(AT)carolina.rr.com)

No other terms below 10^15. [Max Alekseyev, May 20 2012]

Joe K. Crump, 2^n mod n

Cf. A125000, A124974, A033983, A033982, A033981, A050259, A124977, A124965, A015911, A015910.

Cf. A033981, A033982, A033983.

m = 9; Join[Select[Range[m], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^3], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 08 2018 *)

Edited by N. J. A. Sloane, Jun 22 2008, at the suggestion of Don Reble

Terms 1, 7 prepended by Max Alekseyev, May 18 2011

A128121 Numbers k such that 2^k == 5 (mod k).

Original entry on oeis.org

1, 3, 19147, 129505699483, 674344345281, 1643434407157, 5675297754009, 12174063716147, 162466075477787, 313255455573801, 324082741109271

Offset: 1

Alexander Adamchuk, Feb 15 2007

Joe K. Crump, 2^n mod n
OEIS Wiki, 2^n mod n

Cf. A015910, A036236, A050259 (numbers k such that 2^k == 3 (mod k)), A033981, A051447, A033982, A051446, A033983, A128122, A128123, A128124, A128125, A128126.

m = 5; Join[Select[Range[m], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^6], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 08 2018 *)

1 and 3 added by N. J. A. Sloane, Apr 23 2007

Missing a(10) inserted by Sergey Paramonov, Sep 06 2021

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

Original entry on oeis.org

1, 2, 10669, 6611474, 43070220513807782

Offset: 1

Alexander Adamchuk, Feb 15 2007

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

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

Joe K. Crump, 2^n mod n
OEIS Wiki, 2^n mod n

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.

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

1 and 2 added by N. J. A. Sloane, Apr 23 2007

a(5) from Max Alekseyev, Nov 18 2022

A215612 Odd integers n such that 2^n == 2^10 (mod n).

Original entry on oeis.org

1, 7, 73, 9271, 3195367, 6769801, 15413863, 24540337, 47424961, 52268743, 146583343, 384586849, 469501471, 475882081, 859764727, 1097475991, 1169323417, 1400034919, 2518532047, 2870143993, 3258854623, 5609707729, 6022970047, 6420870271, 9011348521

Offset: 1

Max Alekseyev, Aug 17 2012

nonn

Also, the odd solutions to 2^(n-10) == 1 (mod n). The only even solution is n=10.

For all m, 2^A033982(m)-1 belongs to this sequence.

Max Alekseyev, Table of n, a(n) for n = 1..209 (all terms below 10^14)

The odd terms of A015932.

Cf. A173572, A033984, A215610, A215611, A215613

m = 2^10; Join[Select[Range[1, m, 2], Divisible[2^# - m, #] &], Select[Range[m + 1, 10^7, 2], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 15 2018 *)

A051446 Integers n such that 2^n == 13 (mod n).

Original entry on oeis.org

1, 11, 95, 4834519, 156203641, 135466795859, 182901372149135

Offset: 1

Joe K. Crump (joecr(AT)carolina.rr.com)

No other terms below 10^15.

Larger terms: 1910102794991114096035717. - Max Alekseyev, May 18 2011

Cf. A033981, A033982, A033983.

m = 13; Join[Select[Range[m], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^6], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 08 2018 *)

Terms 1, 11 prepended by Max Alekseyev, May 18 2011

a(7) added by Sergey Paramonov, Sep 05 2021

A128123 Numbers k such that 2^k == 10 (mod k).

Original entry on oeis.org

1, 2, 6, 18, 16666, 262134, 4048124214, 24430928839, 243293052886, 41293676570106, 3935632929857549

Offset: 1

Alexander Adamchuk, Feb 15 2007

Some larger terms: 266895924489780149, 2335291686841914329, 18494453435532853111

Joe K. Crump, 2^n mod n

Cf. A015910, A036236, A050259 (numbers k such that 2^k == 3 (mod k)), A033981, A051447, A033982, A051446, A033983, A128121, A128122, A128124, A128125, A128126.

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

1, 2 and 6 added by N. J. A. Sloane, Apr 23 2007
Missing terms a(9)-a(10) added by Max Alekseyev, Dec 16 2013
a(11) from Max Alekseyev, Sep 27 2016

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

Max Alekseyev, Dec 10 2017

nonn

Equivalently, 2^(m+1) == -1 (mod m), or m divides 2^(m+1) + 1.

The sequence is infinite, see A055685.

Chai Wah Wu, Table of n, a(n) for n = 1..1192
OEIS Wiki, 2^n mod n

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)

Select[Range[10^5], Divisible[2^(# + 1) + 1, #] &] (* Robert Price, Oct 11 2018 *)

A296369_list = [n for n in range(1,10**6) if pow(2,n+1,n) == n-1] # Chai Wah Wu, Nov 04 2019

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

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

A128124 Numbers k such that 2^k == 12 (mod k).

Original entry on oeis.org

1, 2, 4, 5, 3763, 125714, 167716, 1803962, 2895548, 4031785, 36226466, 16207566916, 103742264732, 29000474325364, 51053256144532, 219291270961199, 1611547934753332, 5816826177630619

Offset: 1

Alexander Adamchuk, Feb 15 2007

Joe K. Crump, 2^n mod n
OEIS Wiki, 2^n mod n

Cf. A015910, A036236, A050259, A033981, A051447, A033982, A051446, A033983, A128121, A128122, A128123, A128125, A128126.

m = 12; Join[Select[Range[m], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^6], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 08 2018 *)

More terms from Ryan Propper, Mar 23 2007
1, 2, 4 and 5 added by N. J. A. Sloane, Apr 23 2007
a(13)-a(15) from Max Alekseyev, May 19 2011
a(15) corrected, a(16)-a(18) added by Max Alekseyev, Oct 02 2016

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

Robert G. Wilson v

nonn

The odd terms are given by A215612.

For all m, 2^A033982(m)-1 belongs to this sequence.

T. D. Noe, Table of n, a(n) for n = 1..1000
OEIS Wiki, 2^n mod n

Contains A208158 as a subsequence.

Cf. A015919, A015921, A015922, A015924, A015925, A015926, A015927, A015929, A015931, A015935, A015937.

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

Edited by Max Alekseyev, Jul 30 2011

cp's OEIS Frontend

A033983 Integers n such that 2^n == 15 (mod n).

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A051447 Integers n such that 2^n == 9 (mod n).

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A128121 Numbers k such that 2^k == 5 (mod k).

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

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A215612 Odd integers n such that 2^n == 2^10 (mod n).

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A051446 Integers n such that 2^n == 13 (mod n).

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A128123 Numbers k such that 2^k == 10 (mod k).

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

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