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 A257567 a(n) = the highest power of 3 that divides (prime(n)^2+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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Except for n=2, all a(n)>1 because (prime(n)^2+2) is divisible by 3. LINKS Zak Seidov, Table of n, a(n) for n = 1..1000 FORMULA a(n) = A007949(A061725(n)). - Michel Marcus, May 01 2015 EXAMPLE 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. MATHEMATICA Table[IntegerExponent[Prime[k]^2 + 2, 3], {k, 100}] PROG (PARI) a(n) = valuation(prime(n)^2+2, 3); \\ Michel Marcus, May 01 2015 CROSSREFS Cf. A007949 (3-adic valuation), A061725 (p^2+2, with p prime), A257568. Sequence in context: A174820 A099501 A089762 * A318440 A189965 A258820 Adjacent sequences:  A257564 A257565 A257566 * A257568 A257569 A257570 KEYWORD nonn AUTHOR Zak Seidov, Apr 30 2015 STATUS approved

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Last modified April 21 10:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)