A062067 a(1) = 1; a(n) is smallest square > a(n-1) such that a(n) + a(n-1) is a prime.

1, 4, 9, 64, 169, 400, 529, 900, 961, 1936, 2401, 5476, 6241, 6400, 7921, 9216, 10201, 10816, 11025, 13456, 14161, 15376, 17161, 17956, 19321, 19600, 22201, 22500, 24649, 24964, 27225, 29584, 29929, 31684, 33489, 40804, 41209, 52900

Offset: 1

Author

Amarnath Murthy, Jun 12 2001

Keywords

• nonn

Examples

			9 is the next term after 4 as 4+9 = 13 is a prime.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Programs

Mathematica

sqrs=Range[400]^2;
nxt[n_]:=First[Select[sqrs,#>n&&PrimeQ[n+#]&]]
NestList[nxt,1,45]  (* Harvey P. Dale, Dec 26 2010 *)

PARI

p=1;n=2;for(k=1,50, while(!isprime(p^2+n^2),n=n+1);print1(n^2",");p=n;n=n+1)

PARI

{ a=b=1; for (n=1, 1000, if (n>1, until (isprime(a + b^2), b++)); write("b062067.txt", n, " ", a=b^2) ) } \\ Harry J. Smith, Jul 31 2009

Python

from sympy import isprime
A062067, 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
    A062067.append(a**2) # Chai Wah Wu, Sep 01 2014

Extensions

Corrected and extended by Ralf Stephan, Mar 22 2003