OFFSET
1,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..2000
Eric Angelini, Prime squares and square squares, personal blog "Cinquante signes", Jun. 29, 2020.
FORMULA
The sequence is the values of d where 3*d^2+4*d+4, the sum of the four numbers for a square of size d, is prime. For even d this sum will always be even, thus all terms are odd.
EXAMPLE
The board is numbered as follows:
.
1 2 4 7 11 16 .
3 5 8 12 17 .
6 9 13 18 .
10 14 19 .
15 20 .
21 .
.
a(1) = 1 as the four numbers {1,2,5,3} form the corners of a square of size 1, and the sum of these number is 11, a prime number.
a(2) = 3 as the four numbers {1,7,25,10} form the corners of a square of size 3, and the sum of these number is 43, a prime number.
a(3) = 7 as the four numbers {1,29,113,36} form the corners of a square of size 7, and the sum of these number is 179, a prime number.
MATHEMATICA
Select[Range[1, 501, 2], PrimeQ[3#^2+4#+4]&] (* Harvey P. Dale, May 26 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Angelini and Scott R. Shannon, Jul 13 2020
STATUS
approved