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A204769
a(n) = 151*(n-1) - a(n-1) with n>1, a(1)=46.
4
46, 105, 197, 256, 348, 407, 499, 558, 650, 709, 801, 860, 952, 1011, 1103, 1162, 1254, 1313, 1405, 1464, 1556, 1615, 1707, 1766, 1858, 1917, 2009, 2068, 2160, 2219, 2311, 2370, 2462, 2521, 2613, 2672, 2764, 2823
OFFSET
1,1
COMMENTS
Positive numbers k such that k^2 == 2 (mod 151), where the prime 151 == -1 (mod 8).
Equivalently, numbers k such that k == 46 or 105 (mod 151). - Bruno Berselli, Mar 08 2012
FORMULA
G.f.: x*(46+59*x+46*x^2)/((1+x)*(x-1)^2).
a(n) = (-151-33*(-1)^n+302*n)/4.
a(n) = a(n-1) +a(n-2) -a(n-3).
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(59*Pi/302)*Pi/151. - Amiram Eldar, Feb 28 2023
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {46, 105, 197}, 40] (* or *) CoefficientList[Series[x*(46+59*x+46*x^2)/((1+x)*(x-1)^2), {x, 0, 33}], x] (* or *) a[1] = 46; a[n_] := a[n] = 151*(n-1) - a[n-1]; Table[a[n], {n, 1, 40}]
PROG
(Magma) [(-151-33*(-1)^n+302*n)/4: n in [1..60]];
(PARI) a(n)=(-151-33*(-1)^n+302*n)/4 \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
Sequences of the type n^2 == 2 (mod p), where p is a prime of the form 8k-1: A047341, A155450, A164131, A164135, A167533, A167534, A177044, A177046, A204766.
Sequences of the type n^2 == 2 (mod p), where p is a prime of the form 8k+1: A155449, A158803, A159007, A159008, A176010, A206525.
Sequence in context: A050961 A264445 A248529 * A333040 A250778 A118620
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 08 2012
STATUS
approved