A214879 Numbers that cannot be written as sum of the squares of two primes.

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76

Offset: 1

Author

Reinhard Zumkeller, Jul 29 2012

Keywords

• nonn

Comments

A045698(a(n)) = 0.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045636 (complement).

Programs

Haskell

import Data.List (elemIndices)
a214879 n = a214879_list !! (n-1)
a214879_list = elemIndices 0 a045698_list
-- Reinhard Zumkeller, Jul 29 2012

PARI

is(n)=forprime(p=2,sqrtint(n), if(isprimepower(n-p^2)==2, return(0))); 1 \\ Charles R Greathouse IV, Sep 01 2015

Python

from sympy import primerange
def aupto(limit):
    primes = list(primerange(2, int((limit-4)**.5)+2))
    nums = [p*p + q*q for i, p in enumerate(primes) for q in primes[i:]]
    return sorted(set(range(limit+1)) - set(k for k in nums if k <= limit))
print(aupto(76)) # Michael S. Branicky, Aug 13 2021

Formula

a(n) ~ n. - Charles R Greathouse IV, Sep 01 2015