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

1,1

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Cf. A254858.

Sequence in context: A263547 A152819 A297406 * A220888 A289616 A038607

Adjacent sequences: A178135 A178136 A178137 * A178139 A178140 A178141

Keyword

easy,nonn

Author

Jonathan Vos Post, May 20 2010

Status

approved