A287943 - OEIS

%I #36 Aug 09 2017 22:16:31

%S 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,

%T 130,223,160,19,21,62,116,193,322,558,359,23,26,74,144,208,401,868,

%U 713,536,29,30,96,165,238,540,957,1180,1553,2866,31,34,136,186,265,576,1403

%N 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.

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

%H Robert G. Wilson v, <a href="/A287943/b287943.txt">Table of n, a(n) for n = 1..465</a>

%e Row

%e 1:           2          3          5          7         11         13         17

%e 2:           4          6          9         12         15         18         21

%e 3:           5         28         32         53         58         62         74

%e 4:          30         60         68         85        116        144        165

%e 5:          45         64        130        193        208        238        265

%e 6:          97        223        322        401        540        576        765

%e 7:         160        558        868        957       1403       1531       1598

%e 8:         359        713       1180       1467       1639       1808       3131

%e 9:         536       1553       4179       5178       6335       7865       9274

%e 10:       2866       7100      14023      14900      15838      17837      20121

%e 11:       4983      15369      18979      22054      28390      43704      47511

%e 12:      10176      17174      25222      36047      60602      87739     120599

%e 13:      13675      21198     104169     155638     193710     201367     223740

%e 14:     174674     271986     372056     479130     542177     553224     581451

%e 15:     223330     322021     425593     590611     650029     807687     924065

%e 16:     373807     508102     620320     728858     865876    1094922    1133312

%e 17:     564211     674589     797367     980399    1114117    1378160    2055687

%e 18:     619400     735978     888883    1047258    3000375    4135480    5526718

%e 19:     677689    4831099    5819401    7119393    7743933    8367375    9362587

%e 20:    2754394    5325250    6469397    7431663    8055654    8864981   14204980

%e 21:    4039822    6950530   36789607   41026156   43928115   47881364   50592342

%e 22:    5495176   49236853   51408848   61276421   64658379   88092051   96453019

%e 23:   62967400   76375215   92272535  119006122  209296919  261901315  310000824

%e 24:   84323875  235599117  316302735  400483922  497171955  515469235  524697491

%e 25:  159961496  275950926  506320595  520083363  555977282  619254662  638646183

%e 26:  217956211  513201979  587615972  647540001  684757327  812990322 1671545118

%e 27:  365579095  666148664 1242267720 1989912374 2194765721 2371664980 2708581740

%e 28:  954208192 1616090047 2540123360 3262521514 3383785254 3840848685

%e 29: 2901322437 3323153384

%e etc.

%e 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.

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

%Y Cf. A000040, A024675, A036262.

%K nonn,tabl

%O 1,1

%A _Zak Seidov_ and _Robert G. Wilson v_, Jun 03 2017