A254858 - OEIS

A254858

Iterated partial sums of prime numbers, square array read by diagonals.

2, 2, 3, 2, 5, 5, 2, 7, 10, 7, 2, 9, 17, 17, 11, 2, 11, 26, 34, 28, 13, 2, 13, 37, 60, 62, 41, 17, 2, 15, 50, 97, 122, 103, 58, 19, 2, 17, 65, 147, 219, 225, 161, 77, 23, 2, 19, 82, 212, 366, 444, 386, 238, 100, 29, 2, 21, 101, 294, 578, 810, 830, 624, 338, 129, 31

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

Row n+1 = partial sums of row n.

T(n,1) = A002522(n+1); T(n,2) = A144396(n+1); T(n,3) = A002522(n+2).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..7259, first 120 diagonals.

EXAMPLE

. n\k | 1 2 3 4 5 6 7 8 9 10 11 12 13

. ----+------------------------------------------------------------------

. 0 | 2 3 5 7 11 13 17 19 23 29 31 37 41 ..

. 1 | 2 5 10 17 28 41 58 77 100 129 160 197 238 ..

. 2 | 2 7 17 34 62 103 161 238 338 467 627 824 1062 ..

. 3 | 2 9 26 60 122 225 386 624 962 1429 2056 2880 3942 ..

. 4 | 2 11 37 97 219 444 830 1454 2416 3845 5901 8781 12723 ..

. 5 | 2 13 50 147 366 810 1640 3094 5510 9355 15256 24037 36760 ..

. 6 | 2 15 65 212 578 1388 3028 6122 11632 20987 36243 60280 97040 ..

. 7 | 2 17 82 294 872 2260 5288 11410 23042 44029 80272 140552 237592 ...

MATHEMATICA

nmax = 11;

row[0] = Prime[Range[nmax+1]];

row[n_] := row[n] = row[n-1] // Accumulate;

T[n_, k_] := row[n][[k]];

Table[T[n-k, k], {n, 0, nmax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 11 2021 *)

PROG

(Haskell)

a254858_tabl = diags [] $ iterate (scanl1 (+)) a000040_list where

diags uss (vs:vss) = (map head wss) : diags (map tail wss) vss

where wss = vs : uss

a254858_list = concat a254858_tabl

CROSSREFS

Cf. A000040 (row 0), A007504 (row 1), A014148 (row 2), A014150 (row 3), A178138 (row 4), A254784 (row 5).

Cf. A007395 (column 1), A144396 (column 2), A002522 (column 3).

Cf. A125180 (antidiagonal sums), A125179 (diagonals downward).

Sequence in context: A058705 A218699 A090794 * A050323 A318286 A214646

Adjacent sequences: A254855 A254856 A254857 * A254859 A254860 A254861

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Feb 08 2015

STATUS

approved