A083016 - OEIS

%I #13 Dec 09 2019 03:13:08

%S 2,7,29,71,73,251,5,11,53,47,17,19,557,227,97,3,13,23,41,59,137,263,

%T 61,83,113,31,293,107,37,863,433,467,109,1187,257,67,509,167,89,311,

%U 173,151,1613,503,281,43,101,223,353,131,193,383,401,499,797,103,1193,571

%N Rearrangement of primes such that the sum of two consecutive terms is a square.

%C Bunyakovsky's conjecture implies that a(n) always exists. - _Robert Israel_, Dec 08 2019

%H Robert Israel, <a href="/A083016/b083016.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 10^4: # to get all terms before the first term > N

%p Primes:= select(isprime, [seq(i,i=3..N,2)]):

%p A[1]:= 2:

%p for n from 2 do

%p   found:= false;

%p   for k from 1 to nops(Primes) do

%p     if issqr(A[n-1]+Primes[k]) then

%p       A[n]:= Primes[k];

%p       Primes:= subsop(k=NULL,Primes);

%p       found:= true;

%p       break

%p     fi

%p   od;

%p   if not found then break fi

%p od:

%p seq(A[i],i=1..n-1); # _Robert Israel_, Dec 08 2019

%o (PARI) { PS(a)= v=vector(a); v[1]=1; k=prime(1); print1(k","); while(1,t=0; for(s=1,a,r=prime(s); if(v[s]==0 && issquare(k+r),t=r; v[s]=1; break)); if(t==0,break); print1(r","); k=r) }

%K nonn

%O 1,1

%A _Jason Earls_, May 28 2003