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A034794 a(n) is the least prime p > a(n-1) such that a(n-1) is a quadratic residue mod p.

%I A034794 #24 Sep 04 2016 22:52:10
%S A034794 2,7,19,31,41,43,53,59,67,73,79,89,97,101,107,127,139,151,163,173,179,
%T A034794 193,197,223,241,251,283,293,307,313,317,353,383,389,409,419,443,457,
%U A034794 461,467,487,499,521,523,571,577,593,601,607,619,631,641,643,653,659
%N A034794 a(n) is the least prime p > a(n-1) such that a(n-1) is a quadratic residue mod p.
%C A034794 a(n-1) is a term in row a(n) of A046071. - _Reinhard Zumkeller_, May 10 2015
%H A034794 T. D. Noe, <a href="/A034794/b034794.txt">Table of n, a(n) for n=1..1000</a>
%p A034794 f:= proc(t) local i,p;
%p A034794   p:= t;
%p A034794   do
%p A034794     p:= nextprime(p);
%p A034794     if numtheory:-jacobi(t,p) = 1 then return p fi
%p A034794   od
%p A034794 end proc:
%p A034794 A[1]:= 2:
%p A034794 for n from 2 to 100 do A[n]:= f(A[n-1]) od:
%p A034794 seq(A[i],i=1..100); # _Robert Israel_, Sep 04 2016
%t A034794 f[n_] := Block[{k = PrimePi[n] + 1}, While[ JacobiSymbol[n, Prime[k]] == -1, k++ ]; Prime[k]]; NestList[f, 2, 54] (* _Robert G. Wilson v_, Mar 16 2004 *)
%o A034794 (Haskell)
%o A034794 a034794 n = a034794_list !! (n-1)
%o A034794 a034794_list = 2 : f 2 (tail  a000040_list) where
%o A034794    f x (p:ps) = if elem x $ a046071_row p then p : f p ps else f x ps
%o A034794 -- _Reinhard Zumkeller_, May 10 2015
%Y A034794 Cf. A092581.
%Y A034794 Cf. A046071, A000040.
%K A034794 nonn,nice
%O A034794 1,1
%A A034794 _David W. Wilson_
%E A034794 Mathematica updated by _Jean-François Alcover_, Jul 04 2013
%E A034794 Name corrected by _Robert Israel_, Sep 04 2016