login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Least k such that n^k mod k = (n-1)^2, or 0 if no such k exists.
23

%I #34 Mar 15 2015 20:13:24

%S 0,41459,35,9569200211,2673413,10596486211,1885511821439,235,12722173,

%T 1971782729,133617287,14873,1465,1606870609,4247,129015968122421,

%U 526673,835,1079115301,12148589879,12351683,36947690849,6385,5809

%N Least k such that n^k mod k = (n-1)^2, or 0 if no such k exists.

%e a(2) = A036236(1) = 0,

%e a(3) = A078457(2^2) = 41459,

%e a(4) = A119678(3^2) = 35,

%e a(5) = A119679(4^2) = 9569200211,

%e a(6) = A127816(5^2) = 2673413,

%e a(7) = A119715(6^2) = 10596486211,

%e a(8) = A119714(7^2) = 1885511821439,

%e a(9) = A127817(8^2) = 235,

%e a(10) = A127818(9^2) = 12722173,

%e a(11) = A127819(100) = 1971782729,

%e a(12) = A127820(121) = 133617287,

%e a(13) = A127821(144) = 14873,

%e a(14) = A128154(169) = 1465,

%e a(15) = A128155(196) = 1606870609,

%e a(16) = A128156(225) = 4247,

%e a(17) = A128157(256) = 129015968122421,

%e a(18) = A128158(289) = 526673,

%e a(19) = A128159(324) = 835,

%e a(20) = A128160(361) = 1079115301,

%e a(21) = A128361(400) = 12148589879,

%e a(22) = A128362(441) = 12351683,

%e a(23) = A128363(484) = 36947690849,

%e a(24) = A128364(529) = 6385,

%e a(25) = A128365(576) = 5809,

%e a(26) = A128366(625) > 10^15,

%e a(27) = A128367(676) = 299651,

%e a(28) = A128368(729) > 10^14,

%e a(29) = A128369(784) = 2645,

%e a(30) = A128370(841) = 13633321649263,

%e a(31) = A128371(900) = 1051624907,

%e a(32) = A128372(961) = 725521, etc.

%Y Cf. A128148, A128149, A128172, A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128158, A128159, A128160, A128361, A128362, A128363, A128364, A128365, A128366, A128367, A128368, A128369, A128370, A128371, A128372.

%K hard,nonn

%O 2,2

%A _Alexander Adamchuk_, Feb 16 2007, May 06 2007

%E More terms from _Alexander Adamchuk_, Dec 24 2007

%E a(13), a(14), a(16), a(18), a(19), a(24), a(25), a(27), a(29), a(32) from _Alexander Adamchuk_, Feb 17 2008

%E Corrected A-number in cross-reference. Copied a(8) to a(16) from other sequences. - _R. J. Mathar_, Aug 08 2009

%E Edited by _Robert G. Wilson v_, Aug 20 2009

%E a(17) from Joe Crump (joecr(AT)carolina.rr.com), Sep 17 2009.

%E More terms and general editing from _Robert G. Wilson v_, Sep 30 2009

%E a(20)-a(22) from _Robert G. Wilson v_, Oct 17 2009

%E a(23), a(30) from _Max Alekseyev_, Feb 11, Mar 31 2010