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%I #41 Apr 03 2023 10:36:11
%S 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 156,2033,3760,2105,1842,6961,41453,7556,28716,9974,108217,3031,
%U 256669,402707,452111,179537,113178,258898,126198,263183,313608,26616
%N First differences of indices of A000043.
%C First differences of A016027.
%C This sequence is related to the perfect numbers A000396 and the Mersenne primes A000668.
%H A. Booker, <a href="https://t5k.org/nthprime">The Nth Prime Page</a>.
%F a(n) = pi(A000043(n+1)) - pi(A000043(n)), where pi is A000720.
%F a(n) = A016027(n+1) - A016027(n).
%e 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 Differences@ PrimePi@ Array[MersennePrimeExponent, 45] (* _Michael De Vlieger_, Dec 18 2017 *)
%Y Cf. A000043, A000396, A000668, A000720, A016027.
%K nonn
%O 1,4
%A _Omar E. Pol_, Mar 02 2008
%E a(39) (based on update to A016027) from _Ken Takusagawa_, May 31 2011
%E a(40)-a(44) (based on update to A016027) from _Patrick J. McNab_, Jan 27 2018
%E a(45)-a(46) from _Ivan Panchenko_, Apr 12 2018
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