A080478 a(n) = smallest k>a(n-1) such that k^2+a(n-1)^2 is prime, starting with a(1)=1. Square roots of A062067(n).

1, 2, 3, 8, 13, 20, 23, 30, 31, 44, 49, 74, 79, 80, 89, 96, 101, 104, 105, 116, 119, 124, 131, 134, 139, 140, 149, 150, 157, 158, 165, 172, 173, 178, 183, 202, 203, 230, 231, 250, 257, 260, 261, 274, 289, 290, 291, 296, 311, 334, 335, 342, 343, 360, 367, 372

Offset: 1

Author

Ralf Stephan, Mar 22 2003

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (first 2000 terms from Zak Seidov).

Crossrefs

Cf. A073658, A100208, A010051.

Programs

Haskell

a080478 n = a080478_list !! (n-1)
a080478_list = 1 : f 1 [2..] where
   f x (y:ys) | a010051 (x*x + y*y) == 1 = y : (f y ys)
              | otherwise                = f x ys
-- Reinhard Zumkeller, Apr 28 2011

Maple

A[1]:= 1:
for n from 2 to 100 do
  for k from A[n-1]+1 while not isprime(k^2+A[n-1]^2) do od:
  A[n]:= k
od:
seq(A[n],n=1..100); # Robert Israel, Sep 01 2014

Mathematica

nxt[n_]:=Module[{n2=n^2,k=n+1},While[!PrimeQ[k^2+n2],k++];k]; NestList[nxt,1,60] (* Harvey P. Dale, Jun 24 2012 *)
a=1;sq={1}; Do[a2=a^2;b=a+1;While[!PrimeQ[a2+b^2],b=b+2]; AppendTo[sq,b]; a=b,{100}];sq (* Zak Seidov, Feb 21 2014 *)

PARI

p=1;print1(p",");for(n=2,1000, if(isprime(p+n^2),print1(n",");p=n^2))

Python

from sympy import isprime
A080478, a = [1], 1
for _ in range(1,10000):
    a += 1
    b = 2*a*(a-1) + 1
    while not isprime(b):
        b += 4*(a+1)
        a += 2
    A080478.append(a) # Chai Wah Wu, Sep 01 2014

Extensions

PARI program corrected by Zak Seidov, Apr 14 2008