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A155098 Numbers n such that n^2 = -1 mod (41) 6
9, 32, 50, 73, 91, 114, 132, 155, 173, 196, 214, 237, 255, 278, 296, 319, 337, 360, 378, 401, 419, 442, 460, 483, 501, 524, 542, 565, 583, 606, 624, 647, 665, 688, 706, 729, 747, 770, 788, 811, 829, 852, 870, 893, 911, 934, 952, 975, 993, 1016, 1034, 1057 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that n = 9 or 32 mod 41. [Charles R Greathouse IV, Dec 27 2011]

The first pair (a,b) is such that a+b=p, a*b=p*h+1, with h<=(p-1)/4; subsequent pairs are given as (a+kp, b+kp), k=1,2,3...

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

a(n) = 9*(-1)^(n+1) + 41 [n/2]. - M. F. Hasler, Jun 16 2010

a(2k+1) = 41 k + a(1), a(2k) = 41 k - a(1), with a(1) = A002314(6) since 41 = A002144(6). - M. F. Hasler, Jun 16 2010

a(n) = a(n-2)+41 for all n>2. - M. F. Hasler, Jun 16 2010

EXAMPLE

Let p=41, a+b=41, a*b=41h+1, h<=10; for h=7, a+b=41, a*b=41*7+1=288, a=9, b=32; other pairs (9+41, 32+41) and so on.

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {9, 32, 50}, 100] (* Vincenzo Librandi, Feb 29 2012 *)

Select[Range[1100], PowerMod[#, 2, 41] == 40 &] (* Vincenzo Librandi, Apr 24 2014 *)

PROG

(PARI) A155098(n)=n\2*41-9*(-1)^n /* M. F. Hasler, Jun 16 2010 */

CROSSREFS

Cf. A002144, A155086, A155095, A155096, A155097.

Sequence in context: A018833 A130510 A120498 * A063134 A027620 A152619

Adjacent sequences:  A155095 A155096 A155097 * A155099 A155100 A155101

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jan 20 2009

EXTENSIONS

Terms checked & minor edits by M. F. Hasler, Jun 16 2010

STATUS

approved

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Last modified October 20 07:33 EDT 2019. Contains 328252 sequences. (Running on oeis4.)