A178138 Apply partial sum operator 4 times to primes.

2, 11, 37, 97, 219, 444, 830, 1454, 2416, 3845, 5901, 8781, 12723, 18008, 24964, 33972, 45472, 59965, 78019, 100273, 127439, 160308, 199754, 246740, 302326, 367673, 444045, 532813, 635457, 753570, 888872, 1043214, 1218584

Offset: 1

Author

Jonathan Vos Post, May 20 2010

Keywords

• easy
• nonn

Comments

Unlike the results of applying the partial sum operator once (A007504), twice (A014148), or thrice (A014150) to primes, this sequence begins with 4 primes. The next prime in the sequence is a(26) = 367673.

Row 4 in A254858. - Reinhard Zumkeller, Feb 08 2015

Examples

			a(15) = 2 + 9 + 26 + 60 + 122 + 225 + 386 + 624 + 962 + 1429 + 2056 + 2880 + 3942 + 5285 + 6956 = 24964 = 2^2 x 79^2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A007504, A014148, A014150, A178138, A254784.

Cf. A254858.

Programs

Haskell

a178138 n = a178138_list !! (n-1)
a178138_list = (iterate (scanl1 (+)) a000040_list) !! 4
-- Reinhard Zumkeller, Feb 08 2015

Maple

Contribution from R. J. Mathar, Oct 19 2010: (Start)
A007504 := proc(n) option remember; add( ithprime(i),i=1..n) ; end proc:
A014148 := proc(n) option remember; add( A007504(i),i=1..n) ; end proc:
A014150 := proc(n) option remember; add( A014148(i),i=1..n) ; end proc:
A178138 := proc(n) option remember; add( A014150(i),i=1..n) ; end proc: seq(A178138(n),n=1..80) ; (End)

Mathematica

Nest[Accumulate[#]&,Prime[Range[40]],4] (* Harvey P. Dale, Sep 25 2014 *)