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 A083849 #17 Feb 16 2025 08:32:49 %S A083849 2,2,5,5,17,37,101,197,401,677,1601,3137,8101,15877,32401,62501, %T A083849 122501,246017,512657,1020101,2073601,4137157,8386817,16695397, %U A083849 33339077,66977857,133772357,268304401,536663557,1073610757,2146098277 %N A083849 a(n) is the largest prime of the form x^2 + 1 <= 2^n. %C A083849 It is conjectured that this sequence is increasing, but this has never been proved. %C A083849 It is easily shown that all terms greater than 5 end in 1 or 7. %D A083849 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 17. %D A083849 P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 190. %H A083849 Charles R Greathouse IV, <a href="/A083849/b083849.txt">Table of n, a(n) for n = 1..1000</a> %H A083849 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LandausProblems.html">Landau's Problems</a>. %o A083849 (PARI) a(n) = my(last = 2^n+1); while ((p = precprime(last-1)) && (! issquare(p-1)), last = p;); p \\ _Michel Marcus_, Jun 14 2013 %o A083849 (PARI) a(n)=my(k=sqrtint(2^n-1)); while(!isprime(k^2+1), k--); k^2+1 \\ _Charles R Greathouse IV_, Nov 29 2013 %Y A083849 Cf. A005574, A002496, A083844, A083845, A083846, A083847, A083848. %K A083849 nonn %O A083849 1,1 %A A083849 _Harry J. Smith_, May 05 2003