A300854 - OEIS

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

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OFFSET

1,1

COMMENTS

Is a(n) always positive?

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

a(3) = prime(22) = 79 since least k such that A300845(k) = prime(3) = 5 is 22.

MAPLE

f:= proc(p) local q;

q:= 1;

q:= nextprime(q);

if isprime(q^2+q*p+p^2) then return q fi;

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 *)

PROG

(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); }

CROSSREFS

Cf. A300845.

Sequence in context: A016461 A069576 A249678 * A358596 A323745 A109899

Adjacent sequences: A300851 A300852 A300853 * A300855 A300856 A300857

KEYWORD

nonn

AUTHOR

Robert Israel and Altug Alkan, Mar 13 2018

STATUS

approved