A242788 Numbers n such that (n^n-3)/(n-3) is an integer.

1, 2, 4, 5, 6, 7, 9, 11, 13, 15, 16, 27, 31, 33, 36, 55, 73, 91, 133, 241, 249, 366, 367, 491, 513, 577, 733, 757, 871, 913, 971, 991, 1233, 1333, 1576, 1711, 1927, 2071, 2346, 2593, 2731, 3307, 3391, 3529, 4005, 4591, 5113, 5371, 5409, 5671, 5793, 6567, 6801, 7465, 7591

Offset

1,2

Comments

For n > 6, equivalent to n such that n^n = 3 mod n-3. - Chai Wah Wu, Jan 19 2015

Links

Chai Wah Wu, Table of n, a(n) for n = 1..4388

Example

(6^6-3)/(6-3) = 46653/3 = 15551 is an integer. Thus 6 is a member of this sequence.

Mathematica

Select[ Range@ 7600, Mod[ PowerMod[#, #, # - 3] - 3, # - 3] == 0 &] (* Robert G. Wilson v, Jan 21 2015 *)

Prog

(PARI) for(n=1, 10^4, if(n!=3, s=(n^n-3)/(n-3); if(floor(s)==s, print(n))))
(Python)
A242788_list = [1, 2, 4, 5, 6] + [n for n in range(7, 10**6) if pow(n, n, n-3) == 3]
# Chai Wah Wu, Jan 19 2015

Crossrefs

Cf. A242787.

Sequence in context: A242871 A026420 A026479 * A026426 A026480 A126424

Adjacent sequences: A242785 A242786 A242787 * A242789 A242790 A242791

Keyword

nonn

Author

Derek Orr, May 22 2014

Status

approved