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A155097 Numbers n such that n^2 == -1 mod (37) 6
6, 31, 43, 68, 80, 105, 117, 142, 154, 179, 191, 216, 228, 253, 265, 290, 302, 327, 339, 364, 376, 401, 413, 438, 450, 475, 487, 512, 524, 549, 561, 586, 598, 623, 635, 660, 672, 697, 709, 734, 746, 771, 783, 808, 820, 845, 857, 882, 894, 919, 931, 956, 968 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that n = 6 or 31 mod 37. [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) = 6*(-1)^(n+1) + 37 [n/2]. - M. F. Hasler, Jun 16 2010

a(2k+1) = 37 k + a(1), a(2k) = 37 k - a(1), with a(1) = A002314(5) since 37 = A002144(5). - M. F. Hasler, Jun 16 2010

a(n) = a(n-2)+37 for all n>2. - M. F. Hasler, Jun 16 2010

G.f.: x*(6 + 25*x + 6*x^2)/((1 + x)*(1 - x)^2). - Vincenzo Librandi, May 03 2014

EXAMPLE

Let p=37, a+b=37, a*b=37h+1, with h<=9; for h=5, a+b=37, a*b=37*5+1=186, a=6, b=31; other pairs (6+37, 31+37) and so on.

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {6, 31, 43}, 100] (* Vincenzo Librandi, Feb 29 2012 *)

Select[Range[1000], PowerMod[#, 2, 37]==36&] (* Harvey P. Dale, May 06 2012 *)

CoefficientList[Series[(6 + 25 x + 6 x^2)/((1 + x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, May 03 2014 *)

PROG

(PARI) A155097(n)=n\2*37-6*(-1)^n /* M. F. Hasler, Jun 16 2010 */

CROSSREFS

Cf. A002144, A155086, A155095, A155096, A155098.

Sequence in context: A101340 A156825 A043058 * A306331 A254502 A025524

Adjacent sequences:  A155094 A155095 A155096 * A155098 A155099 A155100

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jan 20 2009

EXTENSIONS

Terms checked, a(28) corrected, and minor edits by M. F. Hasler, Jun 16 2010

STATUS

approved

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Last modified January 24 23:49 EST 2021. Contains 340414 sequences. (Running on oeis4.)