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

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, 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, 19, 17, 19, 17, 13, 11, 7, 5, 7, 5, 23, 19, 17, 19, 23, 19, 13

Offset: 1

Author

Reinhard Zumkeller, Feb 22 2015

Keywords

• nonn
• tabl

Comments

All terms are prime by definition of A088643.

See A255313 for sorted distinct terms and A255395 for number of distinct terms.

Examples

			.  n |                  T(n,k)                    |       A255316
. ---+--------------------------------------------+----------------------
.  1 |  3                                         | 3
.  2 |  5  3                                      | 3 5
.  3 |  7  5  3                                   | 3 5  7
.  4 |  7  5  7  5                                | 5 7
.  5 | 11  7  5  7  5                             | 5 7 11
.  6 | 13 11  7  5  7  5                          | 5 7 11 13
.  7 | 13 11 13 11  7  5  3                       | 3 5  7 11 13
.  8 | 17 13 11 13 11  7  5  3                    | 3 5  7 11 13 17
.  9 | 19 17 13 11 13 11  7  5  3                 | 3 5  7 11 13 17 19
. 10 | 19 17 19 17 13 11  7  5  7  5              | 5 7 11 13 17 19
. 11 | 23 19 17 19 17 13 11  7  5  7  5           | 5 7 11 13 17 19 23
. 12 | 23 19 17 19 23 19 13 11  7  5  7  5        | 5 7 11 13 17 19 23
. 13 | 23 19 23 19 17 23 19 11  7 11 13  7  3     | 3 7 11 13 17 19 23
. 14 | 29 23 19 23 19 17 23 19 11  7 11 13  7  3  | 3 7 11 13 17 19 23 29
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A088643, A255316, A255395, A060265.

Programs

Haskell

a255313 n k = a255313_tabl !! (n-1) !! (k-1)
a255313_row n = a255313_tabl !! (n-1)
a255313_tabl = zipWith (zipWith (+)) tss $ map tail tss
               where tss = tail a088643_tabl

Mathematica

(* A is A088643 *)
A[n_, 1] := n;
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[n_] := T[n] = 2 MovingAverage[Table[A[n+1, k], {k, 1, n+1}], {1, 1}];
Array[T, 14] // Flatten (* Jean-François Alcover, Aug 02 2021 *)

Formula

T(n,k) = A088643(n,k-1) + A088643(n,k), 1 <= k <= n;

T(n,1) = A060265(n+1);