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 A135701 #46 Sep 07 2024 08:53:20 %S A135701 1,1,1,2,1,1,3,7,6,4,3,67,13,96,121,11,116,128,19,594,30,131,897,181, %T A135701 156,2033,3760,2105,1842,6961,41453,7556,28716,9974,108217,3031, %U A135701 256669,402707,452111,179537,113178,258898,126198,263183,313608,26616,833014 %N A135701 First differences of indices of A000043. %C A135701 First differences of A016027. %C A135701 This sequence is related to the perfect numbers A000396 and the Mersenne primes A000668. %H A135701 Andrew Booker, <a href="https://t5k.org/nthprime">The Nth Prime Page</a>. %F A135701 a(n) = pi(A000043(n+1)) - pi(A000043(n)), where pi is A000720. %F A135701 a(n) = A016027(n+1) - A016027(n). %e A135701 a(16) = 11 because A000043(16 + 1) = 2281 is the 339 n-th prime, then A016027(16 + 1) = 339 and A000043(16) = 2203 is the 328 n-th prime, then A016027(16) = 328 and we can write 339 - 328 = 11. %t A135701 Differences@ PrimePi@ Array[MersennePrimeExponent, 45] (* _Michael De Vlieger_, Dec 18 2017 *) %Y A135701 Cf. A000043, A000396, A000668, A000720, A016027. %K A135701 nonn %O A135701 1,4 %A A135701 _Omar E. Pol_, Mar 02 2008 %E A135701 a(39) (based on update to A016027) from _Ken Takusagawa_, May 31 2011 %E A135701 a(40)-a(44) (based on update to A016027) from _Patrick J. McNab_, Jan 27 2018 %E A135701 a(45)-a(46) from _Ivan Panchenko_, Apr 12 2018 %E A135701 a(47) from _Amiram Eldar_, Sep 05 2024