cp's OEIS Frontend

A370892 Least positive integer k such that 4 numbers starting with k in an arithmetic progression with difference n have a solution in the game 24.

%I A370892 #35 Mar 29 2024 01:34:32
%S A370892 3,1,1,2,1,1,1,1,2,3,2,1,1,2,2,3,2,12,9,12,2,6,2,2,12,2,2,12,4,12,5,
%T A370892 12,4,12,12,10,12,12,12,12,8,12,12,12,2,12,2,1,8,12,2,12,12,12,12,12,
%U A370892 12,12,12,12,8,12,12,12,12,12,12,12,12,6,5,12,12,12,12,12,12,12,12,12,12,12,12
%N A370892 Least positive integer k such that 4 numbers starting with k in an arithmetic progression with difference n have a solution in the game 24.
%C A370892 24 is a game in which, given 4 four numbers, you must find an expression that evaluates to 24 and contains each of those four numbers exactly once, no other numbers and only the operators of addition, subtraction, multiplication and division.
%C A370892 No term exceeds 12 as for any arithmetic progression 12, 12+n, 12+2n, 12+3n, there is the solution (12)+(12+n)+(12+2n)-(12+3n) = 24.
%C A370892 a(n) = 12 for all n > 144. - _Robert Israel_, Mar 06 2024
%H A370892 Colin Linzer, <a href="https://drive.google.com/file/d/1uFpbi6BIsb91GNk8bwHLZXZzICusnJTE/view?usp=sharing">Java program for the sequence.</a>
%e A370892 For n=4, the arithmetic sequence 1, 5, 9, 13 has the solution (1+5)*(13-9) = 24 so a(4)=1.
%p A370892 nv:= proc(V1,V2)
%p A370892   local a1,a2;
%p A370892   {seq(seq(op([a1+a2,a1*a2,a1-a2,a2-a1]),a1 = V1),a2 = V2),
%p A370892        seq(seq(a1/a2,a1 = V1),a2=V2 minus {0}),
%p A370892        seq(seq(a2/a1,a1 = V1 minus {0}),a2 = V2)}
%p A370892 end proc:
%p A370892 s24:= proc(a,b,c,d) local t;
%p A370892   for t in combinat:-permute([a,b,c,d]) do
%p A370892     if member(24, nv(nv(nv({t[1]},{t[2]}),{t[3]}),{t[4]})) then return true fi;
%p A370892     if member(24, nv(nv({t[1]},{t[2]}),nv({t[3]},{t[4]}))) then return true fi;
%p A370892   od;
%p A370892   false
%p A370892 end proc:
%p A370892 f:= proc(n) local k;
%p A370892   for k from 1 do
%p A370892      if s24(k, k+n, k+2*n, k+3*n) then return k fi;
%p A370892   od;
%p A370892 end proc:
%p A370892 map(f, [$0..100]); # _Robert Israel_, Mar 05 2024
%K A370892 nonn
%O A370892 0,1
%A A370892 _Colin Linzer_, Mar 04 2024