# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a080478 Showing 1-1 of 1 %I A080478 #31 Sep 03 2014 10:38:13 %S A080478 1,2,3,8,13,20,23,30,31,44,49,74,79,80,89,96,101,104,105,116,119,124, %T A080478 131,134,139,140,149,150,157,158,165,172,173,178,183,202,203,230,231, %U A080478 250,257,260,261,274,289,290,291,296,311,334,335,342,343,360,367,372 %N 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). %H A080478 Chai Wah Wu, Table of n, a(n) for n = 1..10000 (first 2000 terms from Zak Seidov). %p A080478 A[1]:= 1: %p A080478 for n from 2 to 100 do %p A080478 for k from A[n-1]+1 while not isprime(k^2+A[n-1]^2) do od: %p A080478 A[n]:= k %p A080478 od: %p A080478 seq(A[n],n=1..100); # _Robert Israel_, Sep 01 2014 %t A080478 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 *) %t A080478 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 *) %o A080478 (PARI) p=1;print1(p",");for(n=2,1000, if(isprime(p+n^2),print1(n",");p=n^2)) %o A080478 (Haskell) %o A080478 a080478 n = a080478_list !! (n-1) %o A080478 a080478_list = 1 : f 1 [2..] where %o A080478 f x (y:ys) | a010051 (x*x + y*y) == 1 = y : (f y ys) %o A080478 | otherwise = f x ys %o A080478 -- _Reinhard Zumkeller_, Apr 28 2011 %o A080478 (Python) %o A080478 from sympy import isprime %o A080478 A080478, a = [1], 1 %o A080478 for _ in range(1,10000): %o A080478 ....a += 1 %o A080478 ....b = 2*a*(a-1) + 1 %o A080478 ....while not isprime(b): %o A080478 ........b += 4*(a+1) %o A080478 ........a += 2 %o A080478 ....A080478.append(a) # _Chai Wah Wu_, Sep 01 2014 %Y A080478 Cf. A073658, A100208, A010051. %K A080478 nonn %O A080478 1,2 %A A080478 _Ralf Stephan_, Mar 22 2003 %E A080478 PARI program corrected by Zak Seidov, Apr 14 2008 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE