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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: A374040 A374478 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 September 19 13:29 EDT 2024. Contains 376012 sequences. (Running on oeis4.)