A182323 a(n) = (194*n + 3*(-1)^n + 1)/4 + 24.

25, 72, 122, 169, 219, 266, 316, 363, 413, 460, 510, 557, 607, 654, 704, 751, 801, 848, 898, 945, 995, 1042, 1092, 1139, 1189, 1236, 1286, 1333, 1383, 1430, 1480, 1527, 1577, 1624, 1674, 1721, 1771, 1818, 1868, 1915, 1965, 2012, 2062, 2109, 2159, 2206, 2256

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

Sequence in context: A032653 A063308 A154050 * A255184 A235941 A337156

Adjacent sequences: A182320 A182321 A182322 * A182324 A182325 A182326

Keyword

nonn,easy

Author

Bruno Berselli, Apr 24 2012

Extensions

Definition changed by Bruno Berselli, Nov 30 2016

Status

approved