A287943 T(1, c) = prime(c). T(r + 1, c) = (T(r, c') + T(r, c'+1)) / 2 where c' is the c-th number such that T(r, c') + T(r, c'+1) is even. Table for T read downwards by antidiagonals.

2, 3, 4, 5, 6, 5, 7, 9, 28, 30, 11, 12, 32, 60, 45, 13, 15, 53, 68, 64, 97, 17, 18, 58, 85, 130, 223, 160, 19, 21, 62, 116, 193, 322, 558, 359, 23, 26, 74, 144, 208, 401, 868, 713, 536, 29, 30, 96, 165, 238, 540, 957, 1180, 1553, 2866, 31, 34, 136, 186, 265, 576, 1403

Offset: 1

Author

Zak Seidov and Robert G. Wilson v, Jun 03 2017

Keywords

• nonn
• tabl

Comments

This array has the same idea as Gilbreath's conjecture (see A036262) but instead of absolute difference it is the integer average sum.

Examples

			Row
1:           2          3          5          7         11         13         17
2:           4          6          9         12         15         18         21
3:           5         28         32         53         58         62         74
4:          30         60         68         85        116        144        165
5:          45         64        130        193        208        238        265
6:          97        223        322        401        540        576        765
7:         160        558        868        957       1403       1531       1598
8:         359        713       1180       1467       1639       1808       3131
9:         536       1553       4179       5178       6335       7865       9274
10:       2866       7100      14023      14900      15838      17837      20121
11:       4983      15369      18979      22054      28390      43704      47511
12:      10176      17174      25222      36047      60602      87739     120599
13:      13675      21198     104169     155638     193710     201367     223740
14:     174674     271986     372056     479130     542177     553224     581451
15:     223330     322021     425593     590611     650029     807687     924065
16:     373807     508102     620320     728858     865876    1094922    1133312
17:     564211     674589     797367     980399    1114117    1378160    2055687
18:     619400     735978     888883    1047258    3000375    4135480    5526718
19:     677689    4831099    5819401    7119393    7743933    8367375    9362587
20:    2754394    5325250    6469397    7431663    8055654    8864981   14204980
21:    4039822    6950530   36789607   41026156   43928115   47881364   50592342
22:    5495176   49236853   51408848   61276421   64658379   88092051   96453019
23:   62967400   76375215   92272535  119006122  209296919  261901315  310000824
24:   84323875  235599117  316302735  400483922  497171955  515469235  524697491
25:  159961496  275950926  506320595  520083363  555977282  619254662  638646183
26:  217956211  513201979  587615972  647540001  684757327  812990322 1671545118
27:  365579095  666148664 1242267720 1989912374 2194765721 2371664980 2708581740
28:  954208192 1616090047 2540123360 3262521514 3383785254 3840848685
29: 2901322437 3323153384
etc.
The 2nd row begins with 4, 6 and 9 since it is the integer average, 4 is the average between 3 and 5, six is the average between 5 and 7, and nine is the average between 7 and 11, etc.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..465

Crossrefs

Cf. A000040, A024675, A036262.

Programs

Mathematica

t = NestList[Select[(Rest@# + Most@#)/2, IntegerQ] &, Prime@ Range@ 1100, 10]; Table[ t[[n -k +1, k]], {n, 11}, {k, n, 1, -1}] // Flatten