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

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

1,1

Comments

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

Links

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

Example

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

Maple

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

Mathematica

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 *)

Prog

(Magma) [n: n in [2..10000] | Denominator((n^n-3)/(n+3)) eq 1];
(PARI) isok(n) = Mod(n, n+3)^n == 3; \\ Michel Marcus, Dec 10 2014
(Sage)
[n for n in range(10^4) if (n + 3).divides((-3)^n - 3)] # Peter Luschny, Jan 17 2015
(Python)
A251862_list = [n for n in range(10**6) if pow(-3, n, n+3) == 3] # Chai Wah Wu, Jan 19 2015

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....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)

Sequence in context: A041437 A302279 A041525 * A363651 A056807 A146927

Adjacent sequences: A251859 A251860 A251861 * A251863 A251864 A251865

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 10 2014

Extensions

More terms from Michel Marcus, Dec 10 2014

Status

approved