cp's OEIS Frontend

A038025 Winner of n-th Littlewood Frog Race.

%I A038025 #17 Apr 18 2020 17:28:25
%S A038025 1,1,1,1,4,1,1,1,1,9,10,1,12,1,1,9,1,1,1,1,4,21,22,1,24,25,1,27,27,1,
%T A038025 1,1,16,1,16,35,32,1,38,9,10,25,33,25,1,45,27,1,25,49,44,25,24,1,1,9,
%U A038025 34,27,1,49,24,1,58,57,64,49,8,49,65,51,48,49,72,69,68
%N A038025 Winner of n-th Littlewood Frog Race.
%C A038025 For 0 < k <= n, gcd(n,k) = 1, let P(n,k) be the smallest prime of the form a*n+k, with a >= 0. "Frog" k0 is said to win "race" n if P(n,k0) is largest of the phi(n) values P(n,k).
%C A038025 In case of draws of P(n,k) values take the largest k. - _R. J. Mathar_, Jul 26 2015
%p A038025 A038025P := proc(n,k)
%p A038025     local a;
%p A038025     for a from 0 do
%p A038025         if isprime(a*n+k) then
%p A038025             return a;
%p A038025         end if;
%p A038025     end do:
%p A038025 end proc:
%p A038025 A038025 := proc(n)
%p A038025     local a,phimax,phi,k ;
%p A038025     a :=0 ;
%p A038025     phimax := 0 ;
%p A038025     for k from 1 to n do
%p A038025         if igcd(k,n) = 1 then
%p A038025             phi := A038025P(n,k) ;
%p A038025             if phi >= phimax then
%p A038025                 a := k;
%p A038025                 phimax := phi;
%p A038025             end if;
%p A038025         end if;
%p A038025     od;
%p A038025     a ;
%p A038025 end proc:
%p A038025 seq(A038025(n),n=1..100) ; # _R. J. Mathar_, Jul 26 2015
%t A038025 A038025P[n_, k_] := Module[{a}, For[a = 0, True, a++, If[PrimeQ[a n + k], Return[a]]]];
%t A038025 A038025[n_] := Module[{a = 0, phiMax = 0, phi, k}, For[k = 1, k <= n, k++, If [GCD[k, n] == 1, phi = A038025P[n, k]; If[phi >= phiMax, a = k; phiMax = phi]]]; a];
%t A038025 Array[A038025, 100] (* _Jean-François Alcover_, Apr 16 2020, after _R. J. Mathar_ *)
%Y A038025 Cf. A038026, A038029 (records).
%K A038025 nonn
%O A038025 1,5
%A A038025 _Christian G. Bower_ from a problem by _David W. Wilson_