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A251603 Numbers n such that n + 2 divides n^n - 2. 4
3, 4551, 46775, 82503, 106976, 1642796, 4290771, 4492203, 4976427, 21537831, 21549347, 21879936, 51127259, 56786087, 60296571, 80837771, 87761787, 94424463, 96593696, 138644871, 168864999, 221395539, 255881451, 297460451, 305198247, 360306363, 562654203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that (n^n - 2)/(n + 2) is an integer.

Since n == -2 (mod n+2), also numbers n such that n + 2 divides (-2)^n - 2. - Robert Israel, Jan 04 2015

Numbers n == 0 (mod 4) such that A066602(n/2+1) = 8, and odd numbers n such that n = 3 or A082493(n+2) = 8. - Robert Israel, Apr 08 2015

LINKS

Table of n, a(n) for n=1..27.

FORMULA

The even terms form A122711, the odd terms are those in A245319 decreased by 2. - Max Alekseyev, Sep 22 2016

EXAMPLE

3 is in this sequence because 3 + 2 = 5 divides 3^3 - 2 = 25.

MAPLE

isA251603 := proc(n)

    if modp(n &^ n-2, n+2) = 0 then

        true;

    else

        false;

    end if;

end proc:

A251603 := proc(n)

    option remember;

    local a;

    if n = 1 then

        3;

    else

        for a from procname(n-1)+1 do

            if isA251603(a) then

                return a;

            end if;

        end do:

    end if;

end proc: # R. J. Mathar, Jan 09 2015

MATHEMATICA

Select[Range[10^6], Mod[PowerMod[#, #, # + 2] - 2, # + 2] == 0 &] (* Michael De Vlieger, Dec 20 2014, based on Robert G. Wilson v at A252041 *)

PROG

(MAGMA) [n: n in [0..10000] | Denominator((n^n-2)/(n+2)) eq 1];

(PARI) for(n=1, 10^9, if(Mod(n, n+2)^n==+2, print1(n, ", "))); \\ Joerg Arndt, Dec 06 2014

(Python)

A251603_list = [n for n in range(1, 10**6) if pow(n, n, n+2) == 2] # Chai Wah Wu, Apr 13 2015

CROSSREFS

Cf. A001477, A004273, A004275, A066602, A082493, A081765, A213382, A252606.

Sequence in context: A094319 A229766 A003166 * A168556 A200950 A307210

Adjacent sequences:  A251600 A251601 A251602 * A251604 A251605 A251606

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Dec 05 2014

EXTENSIONS

Terms 1642796 and beyond from Joerg Arndt, Dec 06 2014

STATUS

approved

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Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)