OFFSET
1,3
COMMENTS
The sequence contains 145 numbers. The numbers < 100 are represented by the form (0,0,0) or (0,0,x) or (0,x,y). The subset of palindromes with three decimal digits of A002113 is included in this sequence.
LINKS
Jinyuan Wang, Table of n, a(n) for n = 1..145
W. Kahan, Computing cross products and rotations in 2 and 3 - dimensional Euclidean spaces, Mathematics and Computer Science Depts. University of California, Berkeley CA 94720 - March 2, 2008.
Eric Weisstein's World of Mathematics, Cross product
FORMULA
From the classical formula of the cross product (or vector product) of two vectors: U = (u1,u2,u3) and V = (v1,v2,v3) with U^V = (u2*v3 - u3*v2, u3*v1 - u1*v3, u1*v2 - u2*v1), we obtain (a,b,c)^(c,b,a) = (a*b-b*c, c^2-a^2, a*b-b*c).
EXAMPLE
2 is in the sequence because (0,0,2)^(2,0,0) = (0*0-2*0, 2*2-0*0, 0*0-0*2) = (0,4,0);
509 is in the sequence because (5,0,9)^(9,0,5) = (0*5-0*9, 9*9-5*5, 5*0-0*9) = (0,56,0).
MAPLE
V:=array(1..3):for n from 0 to 999 do: V[1]:=0: V[2]:=0: V[3]:=0:W:=convert(n, base, 10): if nops(W)=1 then V[1]:=W[1]:else fi:if nops(W)=2 then V[1]:=W[1]: V[2]:=W[2]:else fi:if nops(W)=3 then V[1]:=W[1]: V[2]:=W[2]: V[3]:=W[3]:else fi: if V[3] * V[2] - V[2] * V[1] >= 0 and V[1]^2 - V[3]^2 >=0 then printf(`%d, `, n):else fi:od:
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Michel Lagneau, Dec 07 2011
EXTENSIONS
Offset changed to 1 by Jinyuan Wang, Aug 04 2020
STATUS
approved