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

1,2

Links

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

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 *)

Prog

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

Crossrefs

Cf. A073658, A100208, A010051.

Sequence in context: A217330 A358207 A236169 * A002053 A102315 A142880

Adjacent sequences: A080475 A080476 A080477 * A080479 A080480 A080481

Keyword

nonn

Author

Ralf Stephan, Mar 22 2003

Extensions

PARI program corrected by Zak Seidov, Apr 14 2008

Status

approved