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%I #13 Oct 11 2021 09:05:04
%S 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,
%T 17,2,15,50,97,122,103,58,19,2,17,65,147,219,225,161,77,23,2,19,82,
%U 212,366,444,386,238,100,29,2,21,101,294,578,810,830,624,338,129,31
%N Iterated partial sums of prime numbers, square array read by diagonals.
%C Row n+1 = partial sums of row n.
%C T(n,1) = A002522(n+1); T(n,2) = A144396(n+1); T(n,3) = A002522(n+2).
%H Reinhard Zumkeller, <a href="/A254858/b254858.txt">Table of n, a(n) for n = 0..7259</a>, first 120 diagonals.
%e . n\k | 1 2 3 4 5 6 7 8 9 10 11 12 13
%e . ----+------------------------------------------------------------------
%e . 0 | 2 3 5 7 11 13 17 19 23 29 31 37 41 ..
%e . 1 | 2 5 10 17 28 41 58 77 100 129 160 197 238 ..
%e . 2 | 2 7 17 34 62 103 161 238 338 467 627 824 1062 ..
%e . 3 | 2 9 26 60 122 225 386 624 962 1429 2056 2880 3942 ..
%e . 4 | 2 11 37 97 219 444 830 1454 2416 3845 5901 8781 12723 ..
%e . 5 | 2 13 50 147 366 810 1640 3094 5510 9355 15256 24037 36760 ..
%e . 6 | 2 15 65 212 578 1388 3028 6122 11632 20987 36243 60280 97040 ..
%e . 7 | 2 17 82 294 872 2260 5288 11410 23042 44029 80272 140552 237592 ...
%t nmax = 11;
%t row[0] = Prime[Range[nmax+1]];
%t row[n_] := row[n] = row[n-1] // Accumulate;
%t T[n_, k_] := row[n][[k]];
%t Table[T[n-k, k], {n, 0, nmax}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Oct 11 2021 *)
%o (Haskell)
%o a254858_tabl = diags [] $ iterate (scanl1 (+)) a000040_list where
%o diags uss (vs:vss) = (map head wss) : diags (map tail wss) vss
%o where wss = vs : uss
%o a254858_list = concat a254858_tabl
%Y Cf. A000040 (row 0), A007504 (row 1), A014148 (row 2), A014150 (row 3), A178138 (row 4), A254784 (row 5).
%Y Cf. A007395 (column 1), A144396 (column 2), A002522 (column 3).
%Y Cf. A125180 (antidiagonal sums), A125179 (diagonals downward).
%K nonn,tabl
%O 0,1
%A _Reinhard Zumkeller_, Feb 08 2015
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