A292847 - OEIS

%I #27 Nov 23 2024 18:41:29

%S 5,7,101,11,13,269,17,19,509,23,709,821,29,31,46957,55399,37,

%T 168846239,41,43,9177868096974864412935432937651459122761,47,

%U 485329129,2789,53,3229,3461,59,61,1563353111,139237612541,67,5021,71,73,484639,6221,79,6869,83,7549

%N a(n) is the smallest odd prime of the form ((1 + sqrt(2n))^k - (1 -  sqrt(2n))^k)/(2*sqrt(2n)).

%F When 2n + 3 = p is prime, a(n) = p.

%e For k = {1, 2, 3, 4, 5}, ((1 + sqrt(6))^k - (1 - sqrt(6))^k)/(2*sqrt(6)) = {1, 2, 9, 28, 101}. 101 is odd prime, so a(3) = 101.

%t g[n_, k_] := ((1 + Sqrt[n])^k - (1 - Sqrt[n])^k)/(2Sqrt[n]);

%t Table[k = 3; While[! PrimeQ[Expand@g[2n, k]], k++]; Expand@g[2n, k], {n, 41}]

%Y Cf. A000129, A002605, A015518, A063727, A002532, A083099, A015519, A003683, A002534, A083102, A015520, A091914, A079773, A161007, A099134.

%K nonn

%O 1,1

%A _XU Pingya_, Sep 24 2017