A278180 - OEIS

A278180

Square spiral in which each new term is the sum of its two largest neighbors.

%I #41 Apr 12 2023 10:52:19

%S 1,1,2,3,4,7,8,15,16,17,33,35,37,72,76,80,84,164,172,180,188,368,384,

%T 401,418,435,853,888,925,962,999,1961,2037,2117,2201,2285,2369,4654,

%U 4826,5006,5194,5382,5570,10952,11336,11737,12155,12590,13025,13460,26485,27373,28298,29260,30259,31258,32257,63515

%N Square spiral in which each new term is the sum of its two largest neighbors.

%C To evaluate a(n) consider the neighbors of a(n) that are present in the spiral when a(n) should be a new term in the spiral.

%C For the same idea but for a hexagonal spiral see A278619; and for a right triangle see A278645. It appears that the same idea for an isosceles triangle and also for a square array gives A030237. - _Omar E. Pol_, Dec 04 2016

%H Peter Kagey, <a href="/A278180/b278180.txt">Table of n, a(n) for n = 1..10000</a>

%H Peter Kagey, <a href="/A278180/a278180.png">Bitmap illustrating the parity of the first one million terms</a>. (Even and odd numbers are represented with black and white pixels respeectively.)

%e Illustration of initial terms as a square spiral:

%e .

%e . 84----80----76-----72----37

%e . | |

%e . 164 4-----3-----2 35

%e . | | | |

%e . 172 7 1-----1 33

%e . | | |

%e . 180 8-----15----16----17

%e . |

%e . 188---368---384---401---418

%e .

%e a(21) = 188 because the sum of its two largest neighbors is 180 + 8 = 188.

%e a(22) = 368 because the sum of its two largest neighbors is 180 + 188 = 368.

%e a(23) = 384 because the sum of its two largest neighbors is 368 + 16 = 384.

%e a(24) = 401 because the sum of its two largest neighbors is 384 + 17 = 401.

%e a(25) = 418 because the sum of its two largest neighbors is 401 + 17 = 418.

%e a(26) = 435 because the sum of its two largest neighbors is 418 + 17 = 435.

%Y Cf. A030237, A078510, A141481, A274917, A278181, A278619, A278645.

%K nonn

%O 1,3

%A _Omar E. Pol_, Nov 14 2016