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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

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

EXAMPLE

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.

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

CROSSREFS

Cf. A000040, A024675, A036262.

Sequence in context: A002330 A335130 A305900 * A305211 A091951 A063283

Adjacent sequences:  A287940 A287941 A287942 * A287944 A287945 A287946

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved

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Last modified August 2 17:49 EDT 2021. Contains 346428 sequences. (Running on oeis4.)