A249751 -id:A249751 - cp's OEIS frontend

A252041 Numbers m such that m - 3 divides m^m + 3.

1, 2, 4, 5, 6, 9, 10, 85, 105, 136, 186, 262, 820, 1161, 2626, 2926, 4924, 10396, 11656, 19689, 27637, 33736, 36046, 42886, 42901, 53866, 55189, 82741, 95266, 103762, 106822, 127401, 135460, 251506, 366796, 375220, 413326, 466966, 531445, 553456, 568876

Offset: 1

Juri-Stepan Gerasimov, Dec 12 2014

nonn

Numbers m such that (m^m + 3)/(m - 3) is an integer.
Most but not all terms are congruent to 4 modulo 6. - Robert G. Wilson v, Dec 19 2014
Note that m^m == 3^m (mod m-3). - Robert Israel, Dec 19 2014

			2 is in this sequence because (2^2 + 3)/(2 - 3) = -7 is an integer.
4 is in this sequence because (4^4 + 3)/(4 - 3) = 259 is an integer.
7 is not in the sequence because (7^7 + 3)/4 = 411773/2, which is not an integer.

Robert G. Wilson v, Table of n, a(n) for n = 1..331

Cf. ...............Numbers n such that x divides y, where:
...x......y....k = 0.....k = 1.....k = 2......k = 3.......
..n-k..n^n-k..A000027...A087156...A242787....A242788......
..n-k..n^n+k..A000027..see below..A249751..this sequence..
..n+k..n^n-k..A000027...A004275...A251603....A251862......
..n+k..n^n+k..A000027...A004273...A213382....A242800......
(For x=n-1 and y=n^n+1, the only terms are 0, 2 and 3. - David L. Harden, Dec 28 2014)

[n: n in [4..50000] | Denominator((n^n+3)/(n-3)) eq 1];

select(t -> 3 &^t + 3 mod (t-3) = 0, [1,2,$4..10^6]); # Robert Israel, Dec 19 2014

fQ[n_] := Mod[PowerMod[n, n, n - 3] + 3, n - 3] == 0; Select[Range@ 1000000, fQ] (* Michael De Vlieger, Dec 13 2014; modified by Robert G. Wilson v, Dec 19 2014 *)

isok(n) = (n != 3) && (Mod(n, n-3)^n  == -3); \\ Michel Marcus, Dec 13 2014

More terms from Michel Marcus, Dec 13 2014

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

Original entry on oeis.org

3, 7, 10, 27, 727, 1587, 9838, 758206, 789223, 1018846, 1588126, 1595287, 2387206, 4263586, 9494746, 12697378, 17379860, 21480726, 25439767, 38541526, 44219926, 55561536, 62072326, 64335356, 70032586, 83142466, 85409276

Offset: 1

Juri-Stepan Gerasimov, Dec 10 2014

nonn

m such that m+3 divides (-3)^m - 3. - Robert Israel, Dec 14 2014

			3 is in this sequence because 3 + 3 = 6 divides 3^3 - 3 = 24.

Chai Wah Wu, Table of n, a(n) for n = 1..96

Cf. ...............Numbers n such that x divides y, where:
...x.....y......k=0.......k=1.......k=2........k=3........
..n-k..n^n-k..A000027...A087156...A242787....A242788......
..n-k..n^n+k..A000027..see below..A249751....A252041......
..n+k..n^n-k..A000027...A004275...A251603..this sequence..
..n+k..n^n+k..A000027...A004273...A213382....A242800......
(For x=n-1 and y=n^n+1, the only terms are 0, 2 and 3. - David L. Harden, Jan 14 2015)

[n: n in [2..10000] | Denominator((n^n-3)/(n+3)) eq 1];

select(t ->((-3) &^ (t) - 3) mod (t+3) = 0, [$1..10^6]); # Robert Israel, Dec 14 2014

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 *)

isok(n) = Mod(n, n+3)^n == 3; \\ Michel Marcus, Dec 10 2014

A251862_list = [n for n in range(10**6) if pow(-3, n, n+3) == 3] # Chai Wah Wu, Jan 19 2015

[n for n in range(10^4) if (n + 3).divides((-3)^n - 3)] # Peter Luschny, Jan 17 2015

More terms from Michel Marcus, Dec 10 2014

cp's OEIS Frontend

A252041 Numbers m such that m - 3 divides m^m + 3.

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