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 A298943 #11 Oct 17 2024 12:15:48
%S A298943 2,3,7,19,31,127,607,1279,2281,3217,4423,11213,23209,44497,132049,
%T A298943 216091,1398269,3021377,6972593,13466917,43112609
%N A298943 Lower of two consecutive Mersenne prime exponents with record first difference.
%C A298943 A000043(i) is a term iff A134458(i) is a new record in A134458.
%C A298943 Conjecture: The sequence is infinite.
%H A298943 Wikipedia, <a href="https://en.wikipedia.org/wiki/Mersenne_conjectures#Lenstra%E2%80%93Pomerance%E2%80%93Wagstaff_conjecture">Mersenne conjectures - Lenstra-Pomerance-Wagstaff conjecture</a>.
%e A298943 A000043(7) = 19 and A134458(7) = 12, which is larger than A134458(i) for any i < 7, so 19 is a term of the sequence.
%t A298943 Block[{s = Partition[MersennePrimeExponent@ Range@ 45, 2, 1], t}, t = Map[Differences, s][[All, 1]]; Map[s[[FirstPosition[t, #][[1]] ]] &, Union@ FoldList[Max, t]]][[All, 1]] (* _Michael De Vlieger_, Jan 31 2018 *)
%o A298943 (PARI) LL(e) = my(n, h); n = 2^e-1; h = Mod(2, n); for (k=1, e-2, h=2*h*h-1); return(0==h) \\ after _Joerg Arndt_ in A000043
%o A298943 my(r=0, p=2); forprime(q=3, , if(LL(q), if(q-p > r, print1(p, ", "); r=q-p); p=q))
%Y A298943 Cf. A000043, A134458.
%K A298943 nonn,hard,more
%O A298943 1,1
%A A298943 _Felix Fröhlich_, Jan 30 2018
%E A298943 a(21) from _Amiram Eldar_, Oct 17 2024