login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182739 First differences of the partition numbers of the primes. 1
2, 1, 4, 8, 41, 45, 196, 193, 765, 3310, 2277, 14795, 22946, 18678, 61493, 205177, 501889, 289685, 1558184, 2017516, 1488484, 7662961, 9489819, 26657456, 83235005, 81250196, 56767824, 159900439, 110796851, 309430388, 3062487667, 2050675209, 5133105512 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is the first prime 2, followed by the first differences of the partition numbers of primes.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(1) = 2; a(n) = A000041(A000040(n)) - A000041(A000040(n-1)) for n>1.

EXAMPLE

a(5) = A000041(A000040(5)) - A000041(A000040(4)) = A000041(11) - A000041(7) = 56 - 15 = 41.

MAPLE

with(combinat):

a:= n-> `if`(n=1, 2, (x->x[1]-x[2])(map(numbpart@ithprime, [n, n-1]))):

seq(a(n), n=1..40);  # Alois P. Heinz, Jan 27 2011

MATHEMATICA

Range[40] // Prime // PartitionsP // Differences // Prepend[#, 2]& (* Jean-Fran├žois Alcover, Feb 21 2017 *)

CROSSREFS

Cf. A000040, A000041, A058698.

Sequence in context: A133267 A145864 A306392 * A076014 A120458 A183244

Adjacent sequences:  A182736 A182737 A182738 * A182740 A182741 A182742

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jan 27 2011

EXTENSIONS

More terms from Alois P. Heinz, Jan 27 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)