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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A278505 Square array constructed from Flavius sieve: Each row n (n >= 1) starts with A000960(n), followed by all numbers removed at the stage n of the sieve. 9 1, 2, 3, 4, 5, 7, 6, 11, 9, 13, 8, 17, 21, 15, 19, 10, 23, 33, 37, 25, 27, 12, 29, 45, 55, 51, 31, 39, 14, 35, 57, 75, 85, 73, 43, 49, 16, 41, 69, 97, 111, 121, 99, 61, 63, 18, 47, 81, 115, 145, 159, 151, 127, 67, 79, 20, 53, 93, 135, 171, 199, 211, 193, 163, 87, 91, 22, 59, 105, 157, 205, 243, 267, 271, 247, 187, 103, 109 (list; table; graph; refs; listen; history; text; internal format) OFFSET 1,2 COMMENTS The array A(row,col) is read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ... LINKS Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the array Index entries for sequences that are permutations of the natural numbers Index entries for sequences generated by sieves Index entries for sequences related to the Josephus Problem FORMULA A(row,1) = A000960(row); for col > 1, A(row,col) = A278507(row,col-1). For all n >= 1, A(A278538(n), A278539(n)) = n. EXAMPLE The top left corner of the array: 1, 2, 4, 6, 8, 10, 12, 14, 16, 18 3, 5, 11, 17, 23, 29, 35, 41, 47, 53 7, 9, 21, 33, 45, 57, 69, 81, 93, 105 13, 15, 37, 55, 75, 97, 115, 135, 157, 175 19, 25, 51, 85, 111, 145, 171, 205, 231, 265 27, 31, 73, 121, 159, 199, 243, 283, 327, 367 39, 43, 99, 151, 211, 267, 319, 379, 433, 487 49, 61, 127, 193, 271, 343, 421, 483, 559, 631 63, 67, 163, 247, 339, 427, 519, 607, 691, 793 79, 87, 187, 303, 403, 523, 639, 739, 853, 963 PROG (Scheme) (define (A278505 n) (A278505bi (A002260 n) (A004736 n))) (define (A278505bi row col) (if (= 1 col) (A000960 row) (A278507bi row (- col 1)))) ;; Code for A278507bi given in A278507. CROSSREFS Inverse: A278506. Transpose: A278503. Column 1: A000960, column 2: A100287 (apart from its initial 1), A099259 (differences). Cf. A278538 (row index of n), A278539 (column index of n). Cf. also arrays A278507 and A278511 (different variants). Cf. also A255545 (an analogous array constructed for Lucky sieve). Sequence in context: A369281 A266637 A370496 * A278506 A255546 A358874 Adjacent sequences: A278502 A278503 A278504 * A278506 A278507 A278508 KEYWORD nonn,tabl AUTHOR Antti Karttunen, Nov 23 2016 STATUS approved

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Last modified August 29 23:09 EDT 2024. Contains 375519 sequences. (Running on oeis4.)