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A254858 Iterated partial sums of prime numbers, square array read by diagonals.

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