[seqfan] Re: Filling squares and triangles (with digits)

[юрий герасимов]

Dear Seq Fans, 

I propose to extend Eric's idea. This tdea is called: 

Filling the sides of square or triangle spirals (with digits). 

For square spiral S(n) are 1, 2, 3, 5, 7, 0, 11, 13, 15, 0, 20, 23, 26, 0, 33, 37, 41, 0, 50, 55, 60, 0, 71, 77, 83, 0, 96, 0, 0, 0, 0, 0, 127,0,...

For triangle spiral S(n) are 1, 2, 4, 7, 10, 0, 0, 19, 23, 0, 0, 38, 44, 0, 0, 65, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ....

Without zeros: 1, 2, 4, 7, 19, 23, 38, 44, 65, 73,... What in the next one? 

First differences: 1, 2, 3, 12, 4, 15, 6, 25, 8,... What in the next one? 

Primes in S(n): 2, 7, 19, 23, 73,... What in the next one? 

Example: 

-------------------------------------------------------------------------------- 9, 
-------------------------------------------------------------------------------1, 0, 
----------------------------------------------------------------------------- 9, 5, 9, 
---------------------------------------------------------------------------- 2, 6, 6, 9, 
--------------------------------------------------------------------------- 9, 6, 4, 4, 8, 
-------------------------------------------------------------------------- 3, 6, 4, 4, 6, 8, 
------------------------------------------------------------------------- 9, 7, 5, 2, 3, 3, 8, 
------------------------------------------------------------------------ 4, 6, 4, 8, 7, 4, 6, 7, 
-----------------------------------------------------------------------9, 8, 6, 2, 1, 2, 2, 2, 8, 
--------------------------------------------------------------------- 5, 6, 4, 9, 6, 5, 6, 4, 6, 6,
--------------------------------------------------------------------9, 9, 7, 3, 1, 7, 1, 2, 1, 1, 8,
------------------------------------------------------------------ 6, 7, 4, 0, 7, 8, 6, 4, 5, 4, 6, 5, 
----------------------------------------------------------------- 9, 0, 8, 3, 1, 9, 1, 5, 1, 2, 0, 0, 8, 
-----------------------------------------------------------------7, 7, 4, 1, 8, 1, 2, 3, 4, 3, 4, 4, 6, 4, 
--------------------------------------------------------------- 9, 1, 9, 3, 1, 0, 1, 1, 1, 2, 1, 2, 9, 9, 8, 
-------------------------------------------------------------- 8, 7, 5, 2, 9, 2, 0, 2, 1, 2, 2, 2, 3, 3, 5, 3, 
--------------------------------------------------------------9, 2, 0, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 8, 8, 
------------------------------------------------------------ 9, 7, 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6, 5, 7, 5, 2, 
----------------------------------------------------------- 1, 3, 7, 4, 7, 5, 7, 6, 7, 7, 7, 8, 7, 9, 8, 0, 8, 1, 8, 
----------------------------------------------------------0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 3, ---> 

Best regards, 

JSG.