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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: A275372 A338137 A341289 * 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 November 29 04:38 EST 2021. Contains 349416 sequences. (Running on oeis4.)