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A206525
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a(n) = 113*(n-1) - a(n-1) with n>1, a(1)=51.
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4
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51, 62, 164, 175, 277, 288, 390, 401, 503, 514, 616, 627, 729, 740, 842, 853, 955, 966, 1068, 1079, 1181, 1192, 1294, 1305, 1407, 1418, 1520, 1531, 1633, 1644, 1746, 1757, 1859, 1870, 1972, 1983, 2085, 2096, 2198, 2209
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OFFSET
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1,1
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COMMENTS
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Positive numbers k such that k^2 == 2 (mod 113), where the prime 113 == 1 (mod 8).
Equivalently, numbers k such that k == 51 or 62 (mod 113).
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LINKS
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FORMULA
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a(n) = a(n-2) + 113.
G.f.: x*(51+11*x+51*x^2)/((1+x)*(x-1)^2).
a(n) = (-113-91*(-1)^n+226*n)/4.
a(n) = a(n-1)+a(n-2)-a(n-3).
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(11*Pi/226)*Pi/113. - Amiram Eldar, Feb 28 2023
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MATHEMATICA
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LinearRecurrence[{1, 1, -1}, {51, 62, 164}, 40] (* or *) CoefficientList[Series[x*(51+11*x+51*x^2)/((1+x)*(x-1)^2), {x, 0, 40}], x] (* or *) a[1] = 51; a[n_] := a[n] = 113*(n-1) - a[n-1]; Table[a[n], {n, 1, 40}]
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PROG
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(Magma) [(-113-91*(-1)^n+226*n)/4: n in [1..60]];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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