cp's OEIS Frontend

A293696 Irregular triangle read by rows in which row n lists the partial sums of prime numbers between 2^n+1 and 2^(n+1).

%I A293696 #15 Dec 26 2020 12:34:59
%S A293696 2,3,5,12,11,24,17,36,59,88,119,37,78,121,168,221,280,341,67,138,211,
%T A293696 290,373,462,559,660,763,870,979,1092,1219,131,268,407,556,707,864,
%U A293696 1027,1194,1367,1546,1727,1918,2111,2308,2507,2718,2941,3168,3397,3630,3869,4110,4361
%N A293696 Irregular triangle read by rows in which row n lists the partial sums of prime numbers between 2^n+1 and 2^(n+1).
%H A293696 Olivier Gérard, <a href="/A293696/b293696.txt">Table of n, a(n) for n = 0..6541</a>
%e A293696 The triangle begins
%e A293696 .
%e A293696 2
%e A293696 3
%e A293696 5,12
%e A293696 11,24
%e A293696 17,36,59,88,119
%e A293696 37,78,121,168,221,280,341
%e A293696 67,138,211,290,373,462,559,660,763,870,979,1092,1219
%t A293696 Flatten@Table[
%t A293696   Rest@FoldList[Plus, 0,
%t A293696     Table[Prime[i], {i, PrimePi[2^(n)] + 1, PrimePi[2^(n + 1)]}]], {n,
%t A293696     0, 8}]
%t A293696 Table[Accumulate[Prime[Range[PrimePi[2^n]+1,PrimePi[2^(n+1)]]]],{n,0,10}] // Flatten (* _Harvey P. Dale_, Dec 26 2020 *)
%Y A293696 Cf. A000040, A036378 (length of rows), A293697 (sequence of last item of each row).
%K A293696 nonn,tabf
%O A293696 0,1
%A A293696 _Olivier Gérard_, Oct 15 2017