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 A083847 #21 Feb 16 2025 08:32:49 %S A083847 1,1,2,2,3,4,5,6,8,10,12,14,18,24,33,42,54,70,91,114,158,212,293,393, %T A083847 539,713,957,1301,1792,2459,3378,4615,6233,8418,11540,15867,21729, %U A083847 29843,41169,56534,77697,106787,147067,203025,280340,387308,535153,739671,1023655,1416635,1960813,2716922,3764693,5218926,7238715 %N A083847 a(n) = number of primes of the form x^2 + 1 <= 2^n. %C A083847 It is conjectured that the number of primes of the form x^2+1 is infinite and thus this sequence does not become a constant, but this has never been proved. %D A083847 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 17. %D A083847 P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 190. %H A083847 C. K. Caldwell, <a href="http://www.utm.edu/~caldwell/preprints/Heuristics.pdf">An amazing prime heuristic</a>. %H A083847 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LandausProblems.html">Landau's Problems.</a> %o A083847 (PARI) a(n) = my(nb = 0); forprime(p=2, 2^n, if (issquare(p-1), nb++);); nb \\ _Michel Marcus_, Jun 14 2013 %Y A083847 Cf. A005574, A002496, A083844 - A083849. %K A083847 nonn %O A083847 1,3 %A A083847 _Harry J. Smith_, May 05 2003 %E A083847 More terms from _Alexander D. Healy_, Feb 06 2005