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Winner of n-th Littlewood Frog Race.
8

%I #17 Apr 18 2020 17:28:25

%S 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 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 34,27,1,49,24,1,58,57,64,49,8,49,65,51,48,49,72,69,68

%N Winner of n-th Littlewood Frog Race.

%C 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 In case of draws of P(n,k) values take the largest k. - _R. J. Mathar_, Jul 26 2015

%p A038025P := proc(n,k)

%p local a;

%p for a from 0 do

%p if isprime(a*n+k) then

%p return a;

%p end if;

%p end do:

%p end proc:

%p A038025 := proc(n)

%p local a,phimax,phi,k ;

%p a :=0 ;

%p phimax := 0 ;

%p for k from 1 to n do

%p if igcd(k,n) = 1 then

%p phi := A038025P(n,k) ;

%p if phi >= phimax then

%p a := k;

%p phimax := phi;

%p end if;

%p end if;

%p od;

%p a ;

%p end proc:

%p seq(A038025(n),n=1..100) ; # _R. J. Mathar_, Jul 26 2015

%t A038025P[n_, k_] := Module[{a}, For[a = 0, True, a++, If[PrimeQ[a n + k], Return[a]]]];

%t 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 Array[A038025, 100] (* _Jean-François Alcover_, Apr 16 2020, after _R. J. Mathar_ *)

%Y Cf. A038026, A038029 (records).

%K nonn

%O 1,5

%A _Christian G. Bower_ from a problem by _David W. Wilson_