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
Keywords
Examples
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.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..331
Crossrefs
Cf. ...............Numbers n such that x divides y, where:
...x......y....k = 0.....k = 1.....k = 2......k = 3.......
(For x=n-1 and y=n^n+1, the only terms are 0, 2 and 3. - David L. Harden, Dec 28 2014)
Programs
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Magma
[n: n in [4..50000] | Denominator((n^n+3)/(n-3)) eq 1];
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Maple
select(t -> 3 &^t + 3 mod (t-3) = 0, [1,2,$4..10^6]); # Robert Israel, Dec 19 2014
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Mathematica
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 *)
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PARI
isok(n) = (n != 3) && (Mod(n, n-3)^n == -3); \\ Michel Marcus, Dec 13 2014
Extensions
More terms from Michel Marcus, Dec 13 2014
Comments