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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 9 07:17 EST 2022. Contains 358700 sequences. (Running on oeis4.)