OFFSET
1,5
COMMENTS
For any n > 0 and k > 0, S(n, k) = T(n, k) + T(n, k+1) + T(n+1, k) + T(n+1, k+1) is prime; if (n, k) != (n', k'), then S(n, k) != S(n', k').
T(n, k) is odd iff n > 1 and k > 1 and n or k is odd.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A297617
Rémy Sigrist, Colored representation of T(n, k) for n = 1..500 and k = 1..500 (where the hue is function of T(n, k))
FORMULA
T(n, 1) = 0 for any n > 0.
T(1, k) = 0 for any k > 0.
EXAMPLE
Array T(n, k) begins:
n\k| 1 2 3 4 5 6 7 8 9 10
---+-----------------------------------------------------------
1| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2| 0, 2, 3, 10, 19, 28, 45, 62, 89, 108
3| 0, 1, 5, 5, 9, 15, 15, 27, 15, 39
4| 0, 6, 7, 24, 29, 48, 61, 88, 111, 146
5| 0, 11, 13, 17, 27, 33, 39, 51, 57, 65
6| 0, 20, 15, 44, 43, 76, 85, 118, 147, 180
7| 0, 33, 15, 53, 33, 77, 45, 119, 59, 155
8| 0, 46, 19, 80, 61, 110, 127, 148, 197, 208
9| 0, 63, 35, 89, 47, 135, 61, 185, 87, 235
10| 0, 94, 19, 128, 85, 164, 149, 218, 229, 278
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Jan 01 2018
STATUS
approved