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 A358254 Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that the sum of the eight numbers around any chosen number ends in the chosen number. 3
 0, 1, 2, 3, 4, 5, 6, 7, 12, 8, 9, 10, 11, 13, 15, 23, 14, 16, 18, 21, 17, 19, 29, 25, 33, 20, 22, 26, 28, 120, 24, 27, 87, 58, 125, 88, 30, 31, 97, 124, 45, 187, 32, 34, 73, 132, 55, 49, 42, 35, 36, 95, 195, 59, 98, 863, 37, 38, 130, 104, 129, 62, 736, 67, 39, 40, 115, 131, 48, 748, 82, 208, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The first two numbers placed when a new row or column is formed around the spiral do not complete a 3x3 block of numbers, thus they can be the lowest two numbers that have not appeared. Therefore the sequence a permutation of the nonnegative integers. In the first 10000 terms the largest value is a(8526) = 9874588 while the smallest unused number is 902. LINKS Scott R. Shannon, Table of n, a(n) for n = 0..5000 Eric Angelini, 9 frames and 1 super-frame, personal blog CinquanteSignes.blogspot.com, Oct. 30, 2022. EXAMPLE The square spiral begins: . . 14--23--15--13--11 120 | | | 16 4---3---2 10 28 | | | | | 18 5 0---1 9 26 | | | | 21 6---7--12---8 22 | | 17--19--29--25--33--20 . a(8) = 12 as when the ninth cell is filled it completes a ring of eight numbers around the central cell with number 0, therefore the sum of these eight numbers must end in 0. The sum around the central cell when the eighth cell is filled is 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28, and the lowest unused number that can be added so that the sum ends in 0 is 28 + 12 = 40, so a(8) = 12. a(29) = 120 as when the thirtieth cell is filled the sum of the previous numbers around the number 10 is 13 + 11 + 2 + 28 + 1 + 9 + 26 = 90, and since 20 has already appeared the smallest unused number that can be added to 90 to form a number that ends in 10 is 120. CROSSREFS Cf. A358048, A358021, A358021, A344325, A344367, A354111, A343530. Sequence in context: A271835 A118599 A178531 * A175500 A356253 A222259 Adjacent sequences: A358251 A358252 A358253 * A358255 A358256 A358257 KEYWORD nonn,base AUTHOR Eric Angelini and Scott R. Shannon, Nov 05 2022 STATUS approved

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Last modified September 8 22:43 EDT 2024. Contains 375759 sequences. (Running on oeis4.)