The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A340000 Solution to stacking stones puzzle (see Comments). 2
 1, 17, 33, 46 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is a variant of the stepping stone puzzle sequence (A337663), where you start by placing n 1's on an infinite square grid. Then place the numbers 2,3,... in order on the grid, following the rule that the sum of the 8 surrounding cells has to be equal to the number placed on a cell. a(n) is the largest number which can be achieved starting with n 1's. Additionally, there are 2 different new rules in this "stacking stones" sequence: 1. You can "stack" numbers on top of already placed numbers when the sum of the surrounding 8 cells is equal to the new number. The number inside the cell is not added to the sum and is replaced as value of the cell with the new number. 2. The starting 1's have to be at least one cell apart (to avoid a trivial infinite solution). LINKS S. Brunner, Python program EXAMPLE Illustration for a(3)=33: +------+------+------+------+------+------+------+ |      |      |      |      |      |      |      | |      |      |  18  |  17  |  26  |      |  33  | |      |      |      |  [4] | [13] |      |      | +------+------+------+------+------+------+------+ |      |      |      |      |      |      |      | |      |      |      |   1  |   3  |   5  |  28  | |      |      |      |      |      |      |      | +------+------+------+------+------+------+------+ |      |      |      |      |      |      |      | |      |  21  |  14  |  27  |   2  |  23  |      | |      |      |      |  [6] |      | [11] |      | +------+------+------+------+------+------+------+ |      |      |      |      |      |      |      | |  22  |      |   7  |      |      |   1  |  24  | |      |      |      |      |      |      | [12] | +------+------+------+------+------+------+------+ |      |      |      |      |      |      |      | |      |   1  |   8  |  31  |  32  |      |  25  | |      |      |      | [15] | [16] |      |      | +------+------+------+------+------+------+------+ |  30  |  29  |      |      |      |      |      | | [20] | [19] |      |      |      |      |      | | [10] |  [9] |      |      |      |      |      | +------+------+------+------+------+------+------+ Illustration for a(4)=46: +------+------+------+------+------+------+------+------+------+------+------+------+ |      |      |      |      |      |      |      |      |      |      |      |      | |  32  |      |  37  |  44  |      |      |      |      |      |      |      |      | |      |      | [15] | [22] |      |      |      |      |      |      |      |      | +------+------+------+------+------+------+------+------+------+------+------+------+ |      |      |      |      |      |      |      |      |      |      |      |      | |  24  |   8  |   7  |      |      |  39  |      |      |      |  42  |      |  29  | |      |      |      |      |      |      |      |      |      |      |      |      | +------+------+------+------+------+------+------+------+------+------+------+------+ |      |      |      |  31  |      |      |      |      |      |      |      |      | |      |  16  |   1  | [13] |  18  |  21  |      |      |      |  41  |   1  |  28  | |      |      |      |  [6] |      |      |      |      |      |      |      |      | +------+------+------+------+------+------+------+------+------+------+------+------+ |      |      |      |      |      |      |      |      |      |      |      |      | |      |  17  |      |   2  |   3  |      |      |  43  |      |  40  |      |  27  | |      |      |      |      |      |      |      |      |      | [14] |      |      | +------+------+------+------+------+------+------+------+------+------+------+------+ |      |      |      |      |      |      |      |      |      |      |      |      | |      |  36  |  19  |      |  34  |   4  |   9  |  33  |   1  |  12  |  26  |      | |      |      |      |      |  [1] |      |      | [10] |      |      |      |      | +------+------+------+------+------+------+------+------+------+------+------+------+ |      |      |      |      |      |      |      |      |  46  |      |      |      | |      |      |      |  20  |      |   5  |      |      | [23] |      |  38  |      | |      |      |      |      |      |      |      |      | [11] |      |      |      | +------+------+------+------+------+------+------+------+------+------+------+------+ |      |      |      |      |      |      |      |      |      |      |      |      | |      |      |      |  45  |  25  |  30  |  35  |      |      |      |      |      | |      |      |      |      |      |      |      |      |      |      |      |      | +------+------+------+------+------+------+------+------+------+------+------+------+ CROSSREFS Cf. A337663. Sequence in context: A283395 A244752 A138393 * A044062 A044443 A158057 Adjacent sequences:  A339997 A339998 A339999 * A340001 A340002 A340003 KEYWORD nonn,more,hard AUTHOR S. Brunner, Dec 26 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 22 03:20 EDT 2021. Contains 347605 sequences. (Running on oeis4.)