A135701 First differences of indices of A000043.

1, 1, 1, 2, 1, 1, 3, 7, 6, 4, 3, 67, 13, 96, 121, 11, 116, 128, 19, 594, 30, 131, 897, 181, 156, 2033, 3760, 2105, 1842, 6961, 41453, 7556, 28716, 9974, 108217, 3031, 256669, 402707, 452111, 179537, 113178, 258898, 126198, 263183, 313608, 26616, 833014

Offset: 1

Author

Omar E. Pol, Mar 02 2008

Keywords

• nonn

Comments

First differences of A016027.

This sequence is related to the perfect numbers A000396 and the Mersenne primes A000668.

Examples

			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.
		

Links

• Andrew Booker, The Nth Prime Page.

Crossrefs

Cf. A000043, A000396, A000668, A000720, A016027.

Programs

Mathematica

Differences@ PrimePi@ Array[MersennePrimeExponent, 45] (* Michael De Vlieger, Dec 18 2017 *)

Formula

a(n) = pi(A000043(n+1)) - pi(A000043(n)), where pi is A000720.

a(n) = A016027(n+1) - A016027(n).

Extensions

a(39) (based on update to A016027) from Ken Takusagawa, May 31 2011

a(40)-a(44) (based on update to A016027) from Patrick J. McNab, Jan 27 2018

a(45)-a(46) from Ivan Panchenko, Apr 12 2018

a(47) from Amiram Eldar, Sep 05 2024