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A255313 Triangle read by rows: row n contains the sums of adjacent pairs of terms in row n of A088643.

%I A255313 #13 Aug 04 2021 15:33:31
%S A255313 3,5,3,7,5,3,7,5,7,5,11,7,5,7,5,13,11,7,5,7,5,13,11,13,11,7,5,3,17,13,
%T A255313 11,13,11,7,5,3,19,17,13,11,13,11,7,5,3,19,17,19,17,13,11,7,5,7,5,23,
%U A255313 19,17,19,17,13,11,7,5,7,5,23,19,17,19,23,19,13
%N A255313 Triangle read by rows: row n contains the sums of adjacent pairs of terms in row n of A088643.
%C A255313 All terms are prime by definition of A088643.
%C A255313 See A255313 for sorted distinct terms and A255395 for number of distinct terms.
%H A255313 Reinhard Zumkeller, <a href="/A255313/b255313.txt">Rows n = 1..125 of triangle, flattened</a>
%F A255313 T(n,k) = A088643(n,k-1) + A088643(n,k), 1 <= k <= n;
%F A255313 T(n,1) = A060265(n+1);
%e A255313 .  n |                  T(n,k)                    |       A255316
%e A255313 . ---+--------------------------------------------+----------------------
%e A255313 .  1 |  3                                         | 3
%e A255313 .  2 |  5  3                                      | 3 5
%e A255313 .  3 |  7  5  3                                   | 3 5  7
%e A255313 .  4 |  7  5  7  5                                | 5 7
%e A255313 .  5 | 11  7  5  7  5                             | 5 7 11
%e A255313 .  6 | 13 11  7  5  7  5                          | 5 7 11 13
%e A255313 .  7 | 13 11 13 11  7  5  3                       | 3 5  7 11 13
%e A255313 .  8 | 17 13 11 13 11  7  5  3                    | 3 5  7 11 13 17
%e A255313 .  9 | 19 17 13 11 13 11  7  5  3                 | 3 5  7 11 13 17 19
%e A255313 . 10 | 19 17 19 17 13 11  7  5  7  5              | 5 7 11 13 17 19
%e A255313 . 11 | 23 19 17 19 17 13 11  7  5  7  5           | 5 7 11 13 17 19 23
%e A255313 . 12 | 23 19 17 19 23 19 13 11  7  5  7  5        | 5 7 11 13 17 19 23
%e A255313 . 13 | 23 19 23 19 17 23 19 11  7 11 13  7  3     | 3 7 11 13 17 19 23
%e A255313 . 14 | 29 23 19 23 19 17 23 19 11  7 11 13  7  3  | 3 7 11 13 17 19 23 29
%t A255313 (* A is A088643 *)
%t A255313 A[n_, 1] := n;
%t A255313 A[n_, k_] := A[n, k] = For[m = n-1, m >= 1, m--, If[PrimeQ[m + A[n, k-1]] && FreeQ[Table[A[n, j], {j, 1, k-1}], m], Return[m]]];
%t A255313 T[n_] := T[n] = 2 MovingAverage[Table[A[n+1, k], {k, 1, n+1}], {1, 1}];
%t A255313 Array[T, 14] // Flatten (* _Jean-François Alcover_, Aug 02 2021 *)
%o A255313 (Haskell)
%o A255313 a255313 n k = a255313_tabl !! (n-1) !! (k-1)
%o A255313 a255313_row n = a255313_tabl !! (n-1)
%o A255313 a255313_tabl = zipWith (zipWith (+)) tss $ map tail tss
%o A255313                where tss = tail a088643_tabl
%Y A255313 Cf. A088643, A255316, A255395, A060265.
%K A255313 nonn,tabl
%O A255313 1,1
%A A255313 _Reinhard Zumkeller_, Feb 22 2015