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A252041 Numbers n such that n - 3 divides n^n + 3. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that (n^n + 3)/(n - 3) is an integer.

Most but not all terms are congruent to 4 modulo 6. - Robert G. Wilson v, Dec 19 2014

Note that n^n == 3^n mod (n-3). - Robert Israel, Dec 19 2014

LINKS

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

EXAMPLE

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.

MAPLE

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

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 *)

PROG

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

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

CROSSREFS

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}

Sequence in context: A169694 A285163 A015834 * A231587 A050011 A030303

Adjacent sequences:  A252038 A252039 A252040 * A252042 A252043 A252044

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Dec 12 2014

EXTENSIONS

More terms from Michel Marcus, Dec 13 2014

STATUS

approved

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Last modified May 22 15:13 EDT 2019. Contains 323480 sequences. (Running on oeis4.)