A038025 Winner of n-th Littlewood Frog Race.

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

Offset: 1

Author

Christian G. Bower from a problem by David W. Wilson

Keywords

• nonn

Comments

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).

In case of draws of P(n,k) values take the largest k. - R. J. Mathar, Jul 26 2015

Crossrefs

Cf. A038026, A038029 (records).

Programs

Maple

A038025P := proc(n,k)
    local a;
    for a from 0 do
        if isprime(a*n+k) then
            return a;
        end if;
    end do:
end proc:
A038025 := proc(n)
    local a,phimax,phi,k ;
    a :=0 ;
    phimax := 0 ;
    for k from 1 to n do
        if igcd(k,n) = 1 then
            phi := A038025P(n,k) ;
            if phi >= phimax then
                a := k;
                phimax := phi;
            end if;
        end if;
    od;
    a ;
end proc:
seq(A038025(n),n=1..100) ; # R. J. Mathar, Jul 26 2015

Mathematica

A038025P[n_, k_] := Module[{a}, For[a = 0, True, a++, If[PrimeQ[a n + k], Return[a]]]];
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];
Array[A038025, 100] (* Jean-François Alcover, Apr 16 2020, after R. J. Mathar *)