A300854 a(n) is the smallest prime p = prime(k) such that A300845(k) = prime(n), or 0 if no such k exists.
3, 2, 79, 5, 19, 71, 211, 47, 307, 181, 479, 83, 1231, 293, 547, 1021, 499, 683, 251, 643, 863, 2243, 1009, 1447, 2213, 3361, 4691, 2137, 2657, 2131, 929, 4621, 5851, 1721, 7591, 1901, 11243, 3191, 19501, 3343, 2551, 2927, 997, 4703, 4177, 2789, 14537, 10331, 28723, 36899, 11311, 42433, 29429, 9631
Offset: 1
Keywords
Examples
a(3) = prime(22) = 79 since least k such that A300845(k) = prime(3) = 5 is 22.
Crossrefs
Cf. A300845.
Programs
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Maple
f:= proc(p) local q; q:= 1; do q:= nextprime(q); if isprime(q^2+q*p+p^2) then return q fi; od end proc: V:= Vector(100): p:= 1: count:= 0: while count < 100 do p:= nextprime(p); v:= numtheory:-pi(f(p)); if v <= 100 and V[v] = 0 then V[v]:= p; count:= count+1; fi od: convert(V,list); -
Mathematica
With[{s = Table[Block[{q = 2}, While[! PrimeQ[q^2 + q p + p^2], q = NextPrime@ q]; q], {p, Prime@ Range[10^4]}]}, TakeWhile[#, # > 0 &] &@ Table[Prime@ First@ FirstPosition[s, p] /. k_ /; ! IntegerQ@ k -> -1, {p, Prime@ Range@ PrimePi@ Max@ s}] ] (* Michael De Vlieger, Mar 16 2018 *) -
PARI
a300845(n) = {my(p=prime(n)); forprime(q=2, ,if(isprime(p^2+p*q+q^2), return(q)))} a(n) = {my(k=1); while(a300845(k) != prime(n), k++); prime(k); }
Comments