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A287943
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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This array has the same idea as Gilbreath's conjecture (see A036262) but instead of absolute difference it is the integer average sum.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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t = NestList[Select[(Rest@# + Most@#)/2, IntegerQ] &, Prime@ Range@ 1100, 10]; Table[ t[[n -k +1, k]], {n, 11}, {k, n, 1, -1}] // Flatten
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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