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A260869
Least k > 0 such that k^2 + (prime(n)-k)^2 is a prime, or 0 if no such k exists.
3
1, 1, 1, 1, 1, 3, 1, 2, 3, 2, 5, 1, 1, 3, 2, 4, 2, 3, 1, 6, 3, 4, 4, 2, 2, 3, 3, 5, 7, 3, 1, 1, 2, 2, 2, 1, 1, 3, 10, 3, 2, 1, 3, 3, 10, 7, 1, 3, 7, 7, 4, 9, 1, 1, 1, 8, 2, 1, 2, 1, 8, 4, 1, 3, 5, 5, 8, 6, 5, 2, 3, 2, 10, 4, 5, 3, 5, 1, 1, 2, 10, 1, 1, 4, 12, 4, 2, 2, 6, 5, 1, 2, 7, 1, 12, 4, 2
OFFSET
1,6
COMMENTS
It appears that any prime (and also any odd number > 1, see A260870) can be written as the sum of two positive integers such that the sum of their squares is prime. For an even number > 2 this is obviously not possible since k and 2n-k have the same parity and therefore the sum of their squares is even.
LINKS
EXAMPLE
a(n) = A260870((prime(n)-1)/2) for n > 1. - Robert Israel, Oct 10 2024, corrected by M. F. Hasler, Oct 10 2024
MAPLE
f:= proc(n) local p, k;
p:= ithprime(n);
for k from 1 to p do if isprime(k^2 + (p-k)^2) then return k fi od;
0
end proc:
map(f, [$1..100]); # Robert Israel, Oct 10 2024
PROG
(PARI) A260869(n)=for(k=1, (n=prime(n))\2, isprime(k^2+(n-k)^2)&&return(k))
(Python)
from sympy import prime, isprime
def A260869(n):
p = prime(n)
return next((k for k in range(1, (p>>1)+1) if isprime(k**2+(p-k)**2)), 0) # Chai Wah Wu, Oct 14 2024
CROSSREFS
Cf. A260870.
Sequence in context: A305391 A165084 A029279 * A274514 A342932 A026181
KEYWORD
nonn
AUTHOR
M. F. Hasler, Aug 09 2015
EXTENSIONS
Corrected by Robert Israel, Oct 10 2024
STATUS
approved