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A178138 Apply partial sum operator 4 times to primes.

%I A178138 #12 Feb 08 2015 17:43:17
%S A178138 2,11,37,97,219,444,830,1454,2416,3845,5901,8781,12723,18008,24964,
%T A178138 33972,45472,59965,78019,100273,127439,160308,199754,246740,302326,
%U A178138 367673,444045,532813,635457,753570,888872,1043214,1218584
%N A178138 Apply partial sum operator 4 times to primes.
%C A178138 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.
%C A178138 Row 4 in A254858. - _Reinhard Zumkeller_, Feb 08 2015
%H A178138 Harvey P. Dale, <a href="/A178138/b178138.txt">Table of n, a(n) for n = 1..1000</a>
%e A178138 a(15) = 2 + 9 + 26 + 60 + 122 + 225 + 386 + 624 + 962 + 1429 + 2056 + 2880 + 3942 + 5285 + 6956 = 24964 = 2^2 x 79^2.
%p A178138 Contribution from _R. J. Mathar_, Oct 19 2010: (Start)
%p A178138 A007504 := proc(n) option remember; add( ithprime(i),i=1..n) ; end proc:
%p A178138 A014148 := proc(n) option remember; add( A007504(i),i=1..n) ; end proc:
%p A178138 A014150 := proc(n) option remember; add( A014148(i),i=1..n) ; end proc:
%p A178138 A178138 := proc(n) option remember; add( A014150(i),i=1..n) ; end proc: seq(A178138(n),n=1..80) ; (End)
%t A178138 Nest[Accumulate[#]&,Prime[Range[40]],4] (* _Harvey P. Dale_, Sep 25 2014 *)
%o A178138 (Haskell)
%o A178138 a178138 n = a178138_list !! (n-1)
%o A178138 a178138_list = (iterate (scanl1 (+)) a000040_list) !! 4
%o A178138 -- _Reinhard Zumkeller_, Feb 08 2015
%Y A178138 Cf. A000040, A007504, A014148, A014150, A178138, A254784.
%Y A178138 Cf. A254858.
%K A178138 easy,nonn
%O A178138 1,1
%A A178138 _Jonathan Vos Post_, May 20 2010