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

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

Author

Zak Seidov, Sep 23 2006

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A081765, A015922, A122042.

Programs

Mathematica

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

Extensions

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