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 A134876 #24 Jun 08 2025 03:34:00
%S A134876 1,2,1,3,4,8,18,23,44,73,142,277,484,871,1644,3060,5851,10917,20776,
%T A134876 39263,74752,142521,271223,520242,996486,1916486,3686628,7103236,
%U A134876 13702428,26469008,51193351,99099882,192044541,372559804,723389144
%N A134876 Number of Proth primes: number of primes of the form 1 + k*2^n with k odd and k < 2^n.
%C A134876 The ratio a(n+1)/a(n) is about 2 * n /(n+1). - Corrected by _Thomas Ordowski_, Oct 17 2014
%C A134876 Conjecture: a(n) ~ C * 2^n / n, where C = 1/(2 log 2) = 0.7213475... - _Thomas Ordowski_, Oct 17 2014
%H A134876 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ProthsTheorem.html">Proth's Theorem</a>
%e A134876 a(1)=1 because 3 is the only Proth prime for n=1.
%e A134876 a(2)=2 because 5 and 13 are the only primes for n=2.
%e A134876 a(3)=1 because 41 is the only prime for n=3.
%t A134876 Table[cnt=0; Do[If[PrimeQ[1+k*2^n], cnt++ ], {k,1,2^n,2}]; cnt, {n,20}]
%o A134876 (PARI) a(n) = my(s=0);forstep(k=1,2^n-1,2,s+=ispseudoprime(k<<n+1));s \\ _Jeppe Stig Nielsen_, Jan 19 2020
%Y A134876 Cf. A080076, A331539, A331540.
%K A134876 nonn
%O A134876 1,2
%A A134876 _T. D. Noe_, Nov 17 2007
%E A134876 More terms from _Charles R Greathouse IV_, Mar 18 2010