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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: A168343 A217330 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 3 20:52 EST 2022. Contains 358543 sequences. (Running on oeis4.)