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 A307121 #49 Sep 24 2023 10:41:14
%S A307121 1,4,19,100,581,3912,28091,211700,1655601,13286320,109058381,
%T A307121 911436949,7731247492
%N A307121 Number of Lucasian primes less than 10^n.
%C A307121 The Lucasian primes are those Sophie Germain primes of the form 4k + 3. They are interesting because if they are infinite in number, then the sequence of Mersenne numbers with prime exponents contains an infinite number of composite integers.
%C A307121 Conjecture: about half of all Sophie Germain primes are Lucasian primes, and the rest are either 2 or a prime of the form 4k + 1.
%H A307121 Simon Davis, <a href="http://nntdm.net/volume-20-2014/number-1/19-26/">Arithmetical sequences for the exponents of composite Mersenne numbers</a>, Notes on Number Theory and Discrete Mathematics 20, no. 1 (2014): 19-26.
%e A307121 There are 4 Lucasian primes below 10^2: {3,11,23,83}, therefore a(2) = 4.
%t A307121 c = 0; r = 10; s = {}; Do[If[p > r, AppendTo[s, c]; r *= 10]; If[PrimeQ[p] && PrimeQ[2p + 1], c++], {p, 3, 1000003, 4}]; s (* _Amiram Eldar_, Mar 27 2019 *)
%t A307121 lucSophies = Select[4Range[2500000] - 1, PrimeQ[#] && PrimeQ[2# + 1] &]; Table[Length[Select[lucSophies, # < 10^n &]], {n, 0, 7}]
%o A307121 (PARI) a(n) = { my(t=0); forprime(p=2,10^n,p%4==3 && ispseudoprime(1+(2*p)) && t++);t } \\ _Dana Jacobsen_, Mar 28 2019
%o A307121 (Perl) use ntheory ":all"; sub a { my($n,$t)=(shift,0); forprimes { $t++ if ($_&3) == 3 && is_prime(1+($_<<1)) } 10**$n; $t; } # _Dana Jacobsen_, Mar 28 2019
%Y A307121 Cf. A092816, A002515, A307176.
%K A307121 nonn,more
%O A307121 1,2
%A A307121 _Rodolfo Ruiz-Huidobro_, Mar 26 2019
%E A307121 a(9)-a(11) from _Amiram Eldar_, Mar 27 2019
%E A307121 a(12) from _Amiram Eldar_, Mar 31 2019
%E A307121 a(13) from _Dana Jacobsen_, Apr 02 2019