A161190 Sums of prime points found in four grids in each corner of a square.

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

Author

Enoch Haga, Jun 06 2009, Jun 24 2009, Jun 27 2009

Keywords

• easy
• nonn
• uned

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.

Examples

			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).
		

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.
• Enoch J. Haga, Page 782: drawing 7 lines, 21 points

Crossrefs

Cf. A161191, A161192, A161193, A161194.

Programs

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

Extensions

Partially edited by Jon E. Schoenfield, Feb 26 2013