OFFSET
0,1
COMMENTS
Sequence list the nonnegative numbers k such that k^2 == 43 (mod 97).
Also, numbers k == 25 or 72 (mod 97).
Connected with the solvability of the congruence x^2 == 43 (mod 97) is the unsolvability of x^2 == -1 (mod 11), by the law of quadratic reciprocity.
REFERENCES
Constance Reid, From zero to infinity, The Mathematical Association of America, 1992, 138-141.
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
G.f.: (25 + 47*x + 25*x^2)/((1 + x)*(1 - x)^2).
a(n) = -a(-n-1) = a(n-1) + a(n-2) - a(n-3).
MATHEMATICA
Table[(194 n + 3 (-1)^n + 1)/4 + 24, {n, 0, 46}]
LinearRecurrence[{1, 1, -1}, {25, 72, 122}, 60] (* Harvey P. Dale, Mar 23 2023 *)
PROG
(PARI) Vec((25+47*x+25*x^2)/((1+x)*(1-x)^2)+O(x^47))
(Maxima) a[0]:25$ a[1]:72$ a[2]:122$ a[n]:=a[n-1]+a[n-2]-a[n-3]$ makelist(a[n], n, 0, 46);
(Magma) [n: n in [0..2300] | n^2 mod 97 eq 43];
(Haskell)
a182323 n = a182323_list !! n
a182323_list = filter ((== 43) . (`mod` 97) . (^ 2)) [0..]
-- Reinhard Zumkeller, Apr 25 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Apr 24 2012
EXTENSIONS
Definition changed by Bruno Berselli, Nov 30 2016
STATUS
approved