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A251862 Numbers m such that m + 3 divides m^m - 3.

%I A251862 #49 Jun 28 2024 18:31:52
%S A251862 3,7,10,27,727,1587,9838,758206,789223,1018846,1588126,1595287,
%T A251862 2387206,4263586,9494746,12697378,17379860,21480726,25439767,38541526,
%U A251862 44219926,55561536,62072326,64335356,70032586,83142466,85409276
%N A251862 Numbers m such that m + 3 divides m^m - 3.
%C A251862 m such that m+3 divides (-3)^m - 3. - _Robert Israel_, Dec 14 2014
%H A251862 Chai Wah Wu, <a href="/A251862/b251862.txt">Table of n, a(n) for n = 1..96</a>
%e A251862 3 is in this sequence because 3 + 3 = 6 divides 3^3 - 3 = 24.
%p A251862 select(t ->((-3) &^ (t) - 3) mod (t+3) = 0, [$1..10^6]); # _Robert Israel_, Dec 14 2014
%t A251862 a251862[n_] := Select[Range[n], Mod[PowerMod[#, #, # + 3] - 3, # + 3] == 0 &]; a251862[10^6] (* _Michael De Vlieger_, Dec 14 2014, after _Robert G. Wilson v_ at A252041 *)
%o A251862 (Magma) [n: n in [2..10000] | Denominator((n^n-3)/(n+3)) eq 1];
%o A251862 (PARI) isok(n) = Mod(n, n+3)^n == 3; \\ _Michel Marcus_, Dec 10 2014
%o A251862 (Sage)
%o A251862 [n for n in range(10^4) if (n + 3).divides((-3)^n - 3)] # _Peter Luschny_, Jan 17 2015
%o A251862 (Python)
%o A251862 A251862_list = [n for n in range(10**6) if pow(-3, n, n+3) == 3] # _Chai Wah Wu_, Jan 19 2015
%Y A251862 Cf. ...............Numbers n such that x divides y, where:
%Y A251862 ...x.....y......k=0.......k=1.......k=2........k=3........
%Y A251862 ..n-k..n^n-k..A000027...A087156...A242787....A242788......
%Y A251862 ..n-k..n^n+k..A000027..see below..A249751....A252041......
%Y A251862 ..n+k..n^n-k..A000027...A004275...A251603..this sequence..
%Y A251862 ..n+k..n^n+k..A000027...A004273...A213382....A242800......
%Y A251862 (For x=n-1 and y=n^n+1, the only terms are 0, 2 and 3. - _David L. Harden_, Jan 14 2015)
%K A251862 nonn
%O A251862 1,1
%A A251862 _Juri-Stepan Gerasimov_, Dec 10 2014
%E A251862 More terms from _Michel Marcus_, Dec 10 2014