This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A292847 #31 Apr 13 2025 01:46:24
%S A292847 5,7,101,11,13,269,17,19,509,23,709,821,29,31,46957,55399,37,
%T A292847 168846239,41,43,9177868096974864412935432937651459122761,47,
%U A292847 485329129,2789,53,3229,3461,59,61,1563353111,139237612541,67,5021,71,73,484639,6221,79,6869,83,7549
%N A292847 a(n) is the smallest odd prime of the form ((1 + sqrt(2*n))^k - (1 - sqrt(2*n))^k)/(2*sqrt(2*n)).
%F A292847 When 2*n + 3 = p is prime, a(n) = p.
%e A292847 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 A292847 g[n_, k_] := ((1 + Sqrt[n])^k - (1 - Sqrt[n])^k)/(2Sqrt[n]);
%t A292847 Table[k = 3; While[! PrimeQ[Expand@g[2n, k]], k++]; Expand@g[2n, k], {n, 41}]
%o A292847 (PARI)
%o A292847 g(n,k) = ([0,1;2*n-1,2]^k*[0;1])[1,1]
%o A292847 a(n) = for(k=3,oo,if(ispseudoprime(g(n,k)),return(g(n,k)))) \\ _Jason Yuen_, Apr 12 2025
%Y A292847 Cf. A000129, A002605, A015518, A063727, A002532, A083099, A015519, A003683, A002534, A083102, A015520, A091914, A079773, A161007, A099134.
%K A292847 nonn
%O A292847 1,1
%A A292847 _XU Pingya_, Sep 24 2017