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A161190
Sums of prime points found in four grids in each corner of a square.
5
281, 414, 857, 942, 1124, 2569, 1295, 1433, 1094, 2426, 2730, 3000, 2459, 2575, 1818, 4991, 5331, 3363, 1163, 5006, 5226, 1381, 7213, 7493, 4729, 8217, 3456, 3546, 3684, 5615, 7834, 8090, 6243, 2143, 8862, 11407, 9396, 12019, 4906, 7631, 2591, 13411
OFFSET
1,1
COMMENTS
When the points are marked on drawn lines the concavity is apparent.
The lines are indicated with capital letters A through G (see Fig. 6 in Link)
- A
B 1 7 12 16 19 21
C 2 8 13 17 20
D 3 9 14 18
E 4 10 15
F 5 11
G 6
Reading diagonally across the bottom of the first of 4 diagonals:
6,11,15,18,20,21. The next 3 diagonals are formed by adding 1 to 21, e.g.,
22,27,31,34,36,37
38,43,47,50,52,53
54,59,63,66,68,69. This grid is numbered 1, and the next, 2, starts at 70.
Each numbered set of 4 grids fills the corners of a square delineating and surrounding a circle suggested by the 24 numbers above on its circumference.
LINKS
Enoch J. Haga, On summing the numbers assigned to points in lines of general position, School Science and Mathematics, vol LXIV, no 9, whole 569, Dec 1964 pages 777-782.
EXAMPLE
a(1)=281 because that is the sum of the prime points in the first set of 4 lower diagonals in the first 4 corner grids: (11+31+37+43+47+53+59=281).
PROG
(UBASIC)
10 'rotate points, Enoch Haga, Jun 05 2009
20 F=5
30 A=F+1:print A; :if A=prmdiv(A) then S=S+B:print "*";
40 B=A+5:print B; :if B=prmdiv(B) then S=S+B:print "*";
50 C=B+4:print C; :if C=prmdiv(C) then S=S+C:print "*";
60 D=C+3:print D; :if D=prmdiv(D) then S=S+D:print "*";
70 E=D+2:print E; :if E=prmdiv(E) then S=S+E:print "*";
80 F=E+1:print F; :if F=prmdiv(F) then S=S+F:print "*";
90 R=R+1:if R=4 and S=prmdiv(S) then print S; "*";
100 if R=4 then print R; S; :T=T+1:print T:R=0:S=0
110 stop:goto 30
CROSSREFS
KEYWORD
easy,nonn,uned
AUTHOR
Enoch Haga, Jun 06 2009, Jun 24 2009, Jun 27 2009
EXTENSIONS
Partially edited by Jon E. Schoenfield, Feb 26 2013
STATUS
approved