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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
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
Sequence in context: A144512 A159314 A361707 * A051467 A243716 A356776
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 March 4 14:06 EST 2024. Contains 370532 sequences. (Running on oeis4.)