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Numbers that cannot be written as sum of the squares of two primes.
4

%I #16 Aug 13 2021 08:05:50

%S 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,

%T 30,31,32,33,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,52,54,55,

%U 56,57,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,75,76

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

%C A045698(a(n)) = 0.

%H Reinhard Zumkeller, <a href="/A214879/b214879.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ n. - _Charles R Greathouse IV_, Sep 01 2015

%o (Haskell)

%o import Data.List (elemIndices)

%o a214879 n = a214879_list !! (n-1)

%o a214879_list = elemIndices 0 a045698_list

%o -- _Reinhard Zumkeller_, Jul 29 2012

%o (PARI) is(n)=forprime(p=2,sqrtint(n), if(isprimepower(n-p^2)==2, return(0))); 1 \\ _Charles R Greathouse IV_, Sep 01 2015

%o (Python)

%o from sympy import primerange

%o def aupto(limit):

%o primes = list(primerange(2, int((limit-4)**.5)+2))

%o nums = [p*p + q*q for i, p in enumerate(primes) for q in primes[i:]]

%o return sorted(set(range(limit+1)) - set(k for k in nums if k <= limit))

%o print(aupto(76)) # _Michael S. Branicky_, Aug 13 2021

%Y Cf. A045636 (complement).

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Jul 29 2012