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A366193
For n >= 0, a(n) is the least x >= 0 such that x^2 + (x + 2*n)^2 + 1 = p, p prime number (A000040).
0
1, 0, 0, 0, 1, 0, 9, 0, 0, 6, 0, 6, 0, 0, 3, 15, 1, 2, 0, 1, 0, 6, 1, 2, 6, 3, 9, 0, 0, 6, 15, 4, 5, 0, 3, 2, 6, 0, 2, 3, 1, 9, 0, 4, 3, 0, 7, 0, 3, 1, 6, 6, 1, 5, 6, 0, 2, 6, 0, 6, 0, 1, 0, 0, 13, 0, 6, 0, 6, 3, 4, 11, 12, 0, 3, 0, 9, 3, 0, 3, 0, 21, 9, 2, 3, 0, 6, 18, 0, 3
OFFSET
0,7
COMMENTS
For a(n) = 0 the resulting primes p >= 5 see in A002496.
FORMULA
a(n) = 0 for n from A001912.
EXAMPLE
n = 0: x^2 + x^2 + 1 = p is valid for the least x = 1, p = 3, thus a(0) = 1.
n = 6: x^2 + (x + 12)^2 + 1 = p is valid for the least x = 9, p = 523, thus a(6) = 9.
PROG
(PARI) a(n) = my(x=0); while (!isprime(x^2 + (x + 2*n)^2 + 1), x++); x; \\ Michel Marcus, Oct 03 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Oct 03 2023
EXTENSIONS
More terms from Michel Marcus, Oct 03 2023
STATUS
approved