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

%I A161190 #20 Feb 05 2021 10:33:48
%S A161190 281,414,857,942,1124,2569,1295,1433,1094,2426,2730,3000,2459,2575,
%T A161190 1818,4991,5331,3363,1163,5006,5226,1381,7213,7493,4729,8217,3456,
%U A161190 3546,3684,5615,7834,8090,6243,2143,8862,11407,9396,12019,4906,7631,2591,13411
%N A161190 Sums of prime points found in four grids in each corner of a square.
%C A161190 When the points are marked on drawn lines the concavity is apparent.
%C A161190 The lines are indicated with capital letters A through G (see Fig. 6 in Link)
%C A161190 - A
%C A161190 B 1 7 12 16 19 21
%C A161190 C 2 8 13 17 20
%C A161190 D 3 9 14 18
%C A161190 E 4 10 15
%C A161190 F 5 11
%C A161190 G 6
%C A161190 Reading diagonally across the bottom of the first of 4 diagonals:
%C A161190 6,11,15,18,20,21. The next 3 diagonals are formed by adding 1 to 21, e.g.,
%C A161190 22,27,31,34,36,37
%C A161190 38,43,47,50,52,53
%C A161190 54,59,63,66,68,69. This grid is numbered 1, and the next, 2, starts at 70.
%C A161190 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.
%H A161190 Enoch J. Haga, <a href="https://doi.org/10.1111/j.1949-8594.1964.tb17063.x">On summing the numbers assigned to points in lines of general position</a>, School Science and Mathematics, vol LXIV, no 9, whole 569, Dec 1964 pages 777-782.
%H A161190 Enoch J. Haga, <a href="/A161190/a161190.pdf">Page 782: drawing 7 lines, 21 points</a>
%e A161190 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).
%o A161190 (UBASIC)
%o A161190 10 'rotate points, _Enoch Haga_, Jun 05 2009
%o A161190 20 F=5
%o A161190 30 A=F+1:print A;:if A=prmdiv(A) then S=S+B:print "*";
%o A161190 40 B=A+5:print B;:if B=prmdiv(B) then S=S+B:print "*";
%o A161190 50 C=B+4:print C;:if C=prmdiv(C) then S=S+C:print "*";
%o A161190 60 D=C+3:print D;:if D=prmdiv(D) then S=S+D:print "*";
%o A161190 70 E=D+2:print E;:if E=prmdiv(E) then S=S+E:print "*";
%o A161190 80 F=E+1:print F;:if F=prmdiv(F) then S=S+F:print "*";
%o A161190 90 R=R+1:if R=4 and S=prmdiv(S) then print S;"*";
%o A161190 100 if R=4 then print R;S;:T=T+1:print T:R=0:S=0
%o A161190 110 stop:goto 30
%Y A161190 Cf. A161191, A161192, A161193, A161194.
%K A161190 easy,nonn,uned
%O A161190 1,1
%A A161190 _Enoch Haga_, Jun 06 2009, Jun 24 2009, Jun 27 2009
%E A161190 Partially edited by _Jon E. Schoenfield_, Feb 26 2013