A257567 a(n) is the largest exponent k such that 3^k divides (prime(n)^2 + 2).

1, 0, 3, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 3, 1, 2, 1, 2, 2, 1, 3, 1, 3, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 1, 4, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 2

Offset: 1

Author

Zak Seidov, Apr 30 2015

Keywords

• nonn

Comments

Except for n=2, all a(n) > 1 because (prime(n)^2 + 2) is divisible by 3.

Examples

			a(1) = 1 because p=prime(1)=2 and p^2 + 2 =  6 = 3^1*2,
a(2) = 0 because p=prime(2)=3 and p^2 + 2 = 11 = 3^0*11,
a(3) = 3 because p=prime(3)=5 and p^2 + 2 = 27 = 3^3.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007949 (3-adic valuation), A061725 (p^2+2, with p prime), A257568.

Programs

Mathematica

Table[IntegerExponent[Prime[k]^2 + 2, 3], {k, 100}]

PARI

a(n) = valuation(prime(n)^2+2, 3); \\ Michel Marcus, May 01 2015

Formula

a(n) = A007949(A061725(n)). - Michel Marcus, May 01 2015