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).

2, 3, 5, 12, 11, 24, 17, 36, 59, 88, 119, 37, 78, 121, 168, 221, 280, 341, 67, 138, 211, 290, 373, 462, 559, 660, 763, 870, 979, 1092, 1219, 131, 268, 407, 556, 707, 864, 1027, 1194, 1367, 1546, 1727, 1918, 2111, 2308, 2507, 2718, 2941, 3168, 3397, 3630, 3869, 4110, 4361

Offset

0,1

Links

Olivier Gérard, Table of n, a(n) for n = 0..6541

Example

The triangle begins
.
2
3
5,12
11,24
17,36,59,88,119
37,78,121,168,221,280,341
67,138,211,290,373,462,559,660,763,870,979,1092,1219

Mathematica

Flatten@Table[
  Rest@FoldList[Plus, 0,
    Table[Prime[i], {i, PrimePi[2^(n)] + 1, PrimePi[2^(n + 1)]}]], {n,
    0, 8}]
Table[Accumulate[Prime[Range[PrimePi[2^n]+1, PrimePi[2^(n+1)]]]], {n, 0, 10}] // Flatten (* Harvey P. Dale, Dec 26 2020 *)

Crossrefs

Cf. A000040, A036378 (length of rows), A293697 (sequence of last item of each row).

Sequence in context: A341700 A158936 A271227 * A002139 A140489 A331101

Adjacent sequences: A293693 A293694 A293695 * A293697 A293698 A293699

Keyword

nonn,tabf

Author

Olivier Gérard, Oct 15 2017

Status

approved