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 A071868 #15 Apr 24 2025 01:33:40
%S A071868 1,2,2,3,3,4,4,4,4,5,5,5,5,6,6,7,7,7,7,8,8,8,8,9,9,10,10,10,10,10,10,
%T A071868 10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,
%U A071868 13,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,16,16,16,16
%N A071868 Number of integers k (1 <= k <= n) such that k^2+1 is prime.
%H A071868 Amiram Eldar, <a href="/A071868/b071868.txt">Table of n, a(n) for n = 1..10000</a>
%H A071868 G. H. Hardy and J. E. Littlewood, <a href="https://doi.org/10.1007/BF02403921">Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes</a>, Acta Math., Vol. 44, No. 1 (1923), pp. 1-70. See Section 5.41.
%F A071868 Hardy and Littlewood conjectured that : a(n) ~ c* sqrt(n)/Log(n) where c = Product_{p prime} (1 - (-1)^((p-1)/2)/(p-1)) = 1.3728... (A199401).
%t A071868 Accumulate[Table[If[PrimeQ[k^2+1],1,0],{k,80}]] (* _Harvey P. Dale_, Jan 08 2020 *)
%o A071868 (PARI) for(n=1,200,print1(sum(i=1,n,if(isprime(i^2+1)-1,0,1)),","))
%Y A071868 Cf. A002496, A005574, A199401.
%K A071868 easy,nonn
%O A071868 1,2
%A A071868 _Benoit Cloitre_, Jun 09 2002