

A354441


Lexicographically earliest sequence of distinct positive integers on a square spiral such that any 3X3 square of numbers sums to a prime.


8



1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 10, 13, 12, 14, 20, 16, 15, 17, 19, 22, 18, 21, 25, 26, 35, 23, 24, 27, 28, 30, 29, 31, 33, 37, 41, 36, 32, 34, 43, 38, 40, 52, 39, 42, 66, 48, 45, 44, 46, 47, 49, 54, 50, 56, 51, 57, 53, 55, 61, 72, 67, 59, 58, 62, 60, 63, 71, 68, 74, 76, 70, 80, 64, 65, 69, 77, 73
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OFFSET

1,2


COMMENTS

See A354442 for the successive prime sums formed by each completed 3X3 square of numbers.


LINKS



EXAMPLE

The spiral begins
.
.
32364137333129 57
  
34 1516201412 30 51
    
43 17 543 13 28 56
      
38 19 6 12 10 27 50
     
40 22 78119 24 54
   
52 182125263523 49
 
3942664845444647
.
.
a(9) = 11 as this completes a 3X3 square of numbers 5,4,3,6,1,2,7,8,11, which sum to 47, a prime, and 11 is the smallest unused number to form a prime sum.
a(12) = 13 as this completes a 3X3 square of numbers 8,11,9,1,2,10,4,3,13, which sum to 61, a prime, and 13 is the smallest unused number to form a prime sum.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



