|
|
A206526
|
|
a(n) = 137*(n-1) - a(n-1) with n>1, a(1)=31.
|
|
2
|
|
|
31, 106, 168, 243, 305, 380, 442, 517, 579, 654, 716, 791, 853, 928, 990, 1065, 1127, 1202, 1264, 1339, 1401, 1476, 1538, 1613, 1675, 1750, 1812, 1887, 1949, 2024, 2086, 2161, 2223, 2298, 2360, 2435, 2497, 2572, 2634, 2709, 2771, 2846, 2908, 2983
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Positive numbers k such that k^2 == 2 (mod 137), where the prime 137 == 1 (mod 8).
Equivalently, numbers k such that k == 31 or 106 (mod 137).
The subsequence of primes begins: 31, 853, 1613, 1949, 2161. - Jonathan Vos Post, Mar 09 2012
|
|
LINKS
|
|
|
FORMULA
|
a(n) = a(n-2) + 137.
G.f.: x*(31+75*x+31*x^2)/((1+x)*(x-1)^2).
a(n) = (-137+13*(-1)^n+274*n)/4.
a(n) = a(n-1)+a(n-2)-a(n-3).
Sum_{n>=1} (-1)^(n+1)/a(n) = cot(31*Pi/137)*Pi/137. - Amiram Eldar, Feb 28 2023
|
|
MATHEMATICA
|
LinearRecurrence[{1, 1, -1}, {31, 106, 168}, 40] (* or *) CoefficientList[Series[x*(31+75*x+31*x^2)/((1+x)*(x-1)^2), {x, 0, 50}], x] (* or *) a[1] = 31; a[n_] := a[n] = 137*(n-1) - a[n-1]; Table[a[n], {n, 1, 40}]
|
|
PROG
|
(Magma) [(-137+13*(-1)^n+274*n)/4: n in [1..60]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|