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A135701 First differences of indices of A000043. 0
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 (list; graph; refs; listen; history; text; internal format)
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..46.

A. 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: A228904 A144512 A159314 * A051467 A243716 A333988

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

STATUS

approved

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)