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A182323 a(n) = (194*n + 3*(-1)^n + 1)/4 + 24. 1
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 (list; graph; refs; listen; history; text; internal format)
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}]

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

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Last modified September 28 09:11 EDT 2022. Contains 357068 sequences. (Running on oeis4.)