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 A322049 When A322050 is displayed as a triangle the rows converge to this sequence. 7
 1, 7, 6, 30, 8, 48, 17, 81, 9, 50, 29, 145, 27, 145, 37, 189, 8, 45, 34, 166, 45, 252, 73, 342, 37, 179, 89, 425, 74, 374, 86, 412, 8, 49, 33, 165, 46, 270, 91, 436, 50, 277, 149, 734, 122, 630, 144, 723, 38, 179, 101, 488, 130, 753, 209, 990, 90, 450, 210, 991 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It would be nice to have a formula or recurrence. There is certainly a lot of structure. Indices of records of a(n)/n are (1, 3, 7, 11, 23, 27, 43, 55, 87, 91, 119, 171, 183, 343, 347, 363, 367, 375, 439, 695, 731, 887, 1367, 1371, 1391, 1399, 1451, 1463, 2743, 2923, 2927, 2935, 3511, ...). The ratio a(n)/n increases roughly by 1 at each of these. We conjecture that this ratio is unbounded. We note that the record ratios occur in "clusters" at indices twice as large as the preceding cluster: 87, 91; 171, 183; 343..375; 695..731; 1367..1463; 2743..2935; ... This is compatible with the self-similar structure of the graph of this sequence, which starts over at a(2^k) = 8 for all k >= 4. (But note also the distinctive sub-structure repeating with period 2^10, cf. the "logarithmic plot" link.) - M. F. Hasler, Dec 18 2018 LINKS Hugo Pfoertner, Table of n, a(n) for n = 0..5461 Hugo Pfoertner, Logarithmic plot of 5462 terms, use zoom to see details. FORMULA From M. F. Hasler, Dec 18 2018: (Start) Experimental data suggests the following properties: Sporadic values occurring only a finite number of times, with no regular pattern:   a(n) | 1 | 6 | 7 | 9 |   37   | 48 |  50   | 53 | ...   -----+---+---+---+---+--------+----+-------+----+-----     n  | 0 | 2 | 1 | 8 | 14, 24 |  5 | 9, 40 | 80 | ... Values occurring in regular patterns: a(n) = 8 iff n = 2^k, k = 2 or k >= 4; a(n) > 8 for all other n > 2. a(n) = 33 iff n = 2^(2k+1) + 2, k >= 2; a(n) > 33 for all other n > 12 unless n = 2^k <=> a(n) = 8. a(n) = 34 iff n = 4^k + 2, k >= 2. a(n) = 38 iff n = 3*2^k, k = 4, 5, 6, 8, 10, ... a(n) = 27*2^m if n = 3*2^k with k = 2 (m = 0) or k = 7, 9, ... (m = 1, 2, ...) a(n) = 45 iff n = 20 or n = 4^k + 1, k >= 2. a(n) = 46 iff n = 2^(2k+1) + 4, k >= 2. a(n) = 49 iff n = 2^(2k+1) + 1, k >= 2, or n = 4^k + 4, k >= 3. a(n) > 50 for all n > 10 not mentioned above. (End) CROSSREFS Cf. A319018, A319019, A322048, A322050, A322051. Sequence in context: A299244 A249114 A275372 * A163260 A073112 A070425 Adjacent sequences:  A322046 A322047 A322048 * A322050 A322051 A322052 KEYWORD nonn,look AUTHOR N. J. A. Sloane, Dec 15 2018 STATUS approved

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Last modified August 25 21:00 EDT 2019. Contains 326324 sequences. (Running on oeis4.)