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

1,5

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

Links

Table of n, a(n) for n=1..75.

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 *)

Crossrefs

Cf. A038026, A038029 (records).

Sequence in context: A368884 A350388 A056623 * A079982 A265143 A181873

Adjacent sequences: A038022 A038023 A038024 * A038026 A038027 A038028

Keyword

nonn

Author

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

Status

approved