A015922 -id:A015922 - cp's OEIS frontend

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

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

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

Robert G. Wilson v

nonn

The odd terms are given by A215613.

For all m, 2^A051446(m)-1 belongs to this sequence.

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

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

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

Edited by Max Alekseyev, Jul 31 2011

A245319 Numbers k that divide 2^k + 8.

Original entry on oeis.org

1, 2, 4, 5, 6, 8, 12, 18, 24, 36, 72, 88, 198, 228, 1032, 2412, 2838, 4553, 5958, 10008, 24588, 25938, 46777, 65538, 75468, 82505, 130056, 143916, 200364, 540738, 598818, 750852, 797478, 923628, 958212, 1151538, 1250568, 1505388, 1647396, 2365128, 2964036, 3490028, 3704418, 3844808

Offset: 1

Derek Orr, Jul 17 2014

nonn

			2^4 + 8 = 24 is divisible by 4. Thus 4 is a term of this sequence.
2^5 + 8 = 40 is divisible by 5. Thus 5 is a term of this sequence.

Chai Wah Wu, Table of n, a(n) for n = 1..929 (terms 1..58 from Harvey P. Dale)
OEIS Wiki, 2^n mod n

The odd terms form A357125.

Cf. A015922.

select(n -> 2 &^ n + 8 mod n = 0, [$1..10^6]); # Robert Israel, Jul 18 2014

Join[Select[Range[7],Divisible[2^#+8,#]&],Select[Range[4000000], Abs[ PowerMod[ 2,#,#]-#]==8&]] (* Harvey P. Dale, May 25 2016 *)

for(n=1,10^9,if(Mod(2,n)^n==Mod(-8,n),print1(n,", ")));

A276967 Odd integers n such that 2^n == 2^3 (mod n).

Original entry on oeis.org

1, 3, 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 195, 201, 213, 219, 237, 249, 267, 291, 303, 309, 315, 321, 327, 339, 381, 393, 399, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 693, 699, 717, 723, 731, 753, 771, 789, 807

Offset: 1

Max Alekseyev, Sep 22 2016

Also, integers n such that 2^(n - 3) == 1 (mod n).
Contains A033553 as a subsequence. Smallest term greater than 3 missing in A033553 is 731.
For all m, 2^A015921(m) - 1 belongs to this sequence.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

The odd terms of A015922.

Odd integers n such that 2^n == 2^k (mod n): A176997 (k = 1), A173572 (k = 2), this sequence (k = 3), A033984 (k = 4), A276968 (k = 5), A215610 (k = 6), A276969 (k = 7), A215611 (k = 8), A276970 (k = 9), A215612 (k = 10), A276971 (k = 11), A215613 (k = 12).

Join[{1}, Select[Range[1, 1023, 2], PowerMod[2, # - 3, #] == 1 &]] (* Alonso del Arte, Sep 22 2016 *)

isok(n) = (n % 2) && (Mod(2,n)^n==8); \\ Michel Marcus, Sep 23 2016

A276969 Odd integers n such that 2^n == 2^7 (mod n).

Original entry on oeis.org

1, 3, 7, 15, 49, 91, 133, 217, 255, 259, 301, 427, 469, 511, 527, 553, 679, 721, 763, 889, 973, 1015, 1057, 1099, 1141, 1267, 1351, 1393, 1477, 1561, 1603, 1687, 1897, 1939, 1981, 2107, 2149, 2191, 2317, 2359, 2443, 2569, 2611, 2653, 2779, 2863, 2947, 3031, 3073, 3199, 3241, 3409, 3493, 3661, 3787

Offset: 1

Max Alekseyev, Sep 22 2016

Also, integers n such that 2^(n-7) == 1 (mod n).
Contains A208155 as a subsequence.
For all m, 2^A015922(m)-1 belongs to this sequence.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

The odd terms of A015927.
Odd integers n such that 2^n == 2^k (mod n): A176997 (k=1), A173572 (k=2), A276967 (k=3), A033984 (k=4), A276968 (k=5), A215610 (k=6), this sequence (k=7), A215611 (k=8), A276970 (k=9), A215612 (k=10), A276971 (k=11), A215613 (k=12).
Cf. A015922, A208155.

m = 2^7; Join[Select[Range[1, m, 2], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^3, 2], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 12 2018 *)

is(n)=n%2 && Mod(2,n)^n==128 \\ Charles R Greathouse IV, Sep 22 2016

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

Max Alekseyev, Dec 11 2017

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.

OEIS Wiki, 2^n mod n

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)

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

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

A277344 3-Knödel numbers (A033553) that are not divisible by 3.

Original entry on oeis.org

50963, 5834755, 9835843, 155627923, 245056003, 332852435, 556268443, 724014203, 795650963, 831912763, 2440444163, 4080848203, 5067702643, 5140068643, 5555216803, 7461332483, 8438160643, 11766788323, 11951765003, 13058213003, 13483943203, 14528402983, 16644521435, 17847852803

Offset: 1

Max Alekseyev, Oct 09 2016

nonn

Max Alekseyev, Table of n, a(n) for n = 1..775 (all terms below 10^16)

Intersection of A033553 and A242865.
Intersection of A033553 and A130133.
Subsequence of A015922.

A122711 Even numbers n such that n+2 divides n+2^n.

Original entry on oeis.org

106976, 1642796, 21879936, 96593696, 6926872352, 21235295216, 24936246176, 25867010016, 80832867116, 82230049056, 208329074876, 360598467776, 533800559216, 587627376176, 661575990912, 662312961696, 664490433776, 737374205276, 831623487276, 1052816473676, 1137732817376, 1213045642656, 1270015920636

Offset: 1

Zak Seidov, Sep 23 2006

nonn

Same as even numbers n such that 2^n == 2 (mod n+2). - Robert G. Wilson v, Sep 27 2006
n must be a multiple of 4. A002326(n/4) must not be divisible by 2 or 3. If p is an odd prime factor of n+2, (n+2)/p mod A002326((p-1)/2)=3. - Martin Fuller, Oct 09 2006
Also, the positive numbers A015922(k)-2 that are multiples of 4. E.g., a(1) = 106976 = A015922(3926)-2. Hence, a(n)+2 forms a subsequence of A015922 (and of A130134) consisting of the terms congruent to 2 modulo 4. - Max Alekseyev, Apr 03 2014

Max Alekseyev, Table of n, a(n) for n = 1..110 (all terms below 10^15)

Cf. A081765, A015922, A122042.

Do[ If[ PowerMod[2, 2n, 2n + 2] == 2, Print@2n], {n, 10^9}] (* Robert G. Wilson v, Sep 27 2006 *)

More terms from Max Alekseyev, Sep 23 2006, Oct 01 2006
More terms from Martin Fuller, Oct 09 2006
Terms a(18) onward from Max Alekseyev, Apr 09 2014
b-file corrected by Max Alekseyev, Oct 11 2016

A334634 Numbers m that divide 2^m + 11.

Original entry on oeis.org

1, 13, 16043199041, 91118493923, 28047837698634913

Offset: 1

Max Alekseyev, Sep 10 2020

Equivalently, numbers m such that 2^m == -11 (mod m).

No other terms below 10^17.

OEIS Wiki, 2^n mod n

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).

a(5) from Sergey Paramonov, Oct 10 2021

cp's OEIS Frontend

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

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

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A245319 Numbers k that divide 2^k + 8.

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A276967 Odd integers n such that 2^n == 2^3 (mod n).

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A276969 Odd integers n such that 2^n == 2^7 (mod n).

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

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A277344 3-Knödel numbers (A033553) that are not divisible by 3.

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A122711 Even numbers n such that n+2 divides n+2^n.

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A334634 Numbers m that divide 2^m + 11.

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