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

2, 7, 19, 31, 41, 43, 53, 59, 67, 73, 79, 89, 97, 101, 107, 127, 139, 151, 163, 173, 179, 193, 197, 223, 241, 251, 283, 293, 307, 313, 317, 353, 383, 389, 409, 419, 443, 457, 461, 467, 487, 499, 521, 523, 571, 577, 593, 601, 607, 619, 631, 641, 643, 653, 659

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• nice

Comments

a(n-1) is a term in row a(n) of A046071. - Reinhard Zumkeller, May 10 2015

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A092581.

Cf. A046071, A000040.

Programs

Haskell

a034794 n = a034794_list !! (n-1)
a034794_list = 2 : f 2 (tail  a000040_list) where
   f x (p:ps) = if elem x $ a046071_row p then p : f p ps else f x ps
-- Reinhard Zumkeller, May 10 2015

Maple

f:= proc(t) local i,p;
  p:= t;
  do
    p:= nextprime(p);
    if numtheory:-jacobi(t,p) = 1 then return p fi
  od
end proc:
A[1]:= 2:
for n from 2 to 100 do A[n]:= f(A[n-1]) od:
seq(A[i],i=1..100); # Robert Israel, Sep 04 2016

Mathematica

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 *)

Extensions

Mathematica updated by Jean-François Alcover, Jul 04 2013

Name corrected by Robert Israel, Sep 04 2016