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

1,4

Comments

First differences of A016027.

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

Links

Table of n, a(n) for n=1..47.

Andrew Booker, The Nth Prime Page.

Formula

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

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A144512 A159314 A361707 * A051467 A243716 A356776

Adjacent sequences: A135698 A135699 A135700 * A135702 A135703 A135704

Keyword

nonn

Author

Omar E. Pol, Mar 02 2008

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

Status

approved