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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).
5
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
KEYWORD
nonn
AUTHOR
Ralf Stephan, Mar 22 2003
EXTENSIONS
PARI program corrected by Zak Seidov, Apr 14 2008
STATUS
approved