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A038025
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Winner of n-th Littlewood Frog Race.
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8
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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
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OFFSET
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1,5
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COMMENTS
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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
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LINKS
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MAPLE
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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:
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:
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MATHEMATICA
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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];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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