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A039701
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a(n) = n-th prime modulo 3.
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23
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2, 0, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If n>2 and prime(n) is a Mersenne prime then a(n)=1. Proof: prime(n) = 2^p-1 for some odd prime p, so prime(n) = 2*4^((p-1)/2) - 1 == 2-1 = 1 (mod 3). - Santi Spadaro (spados(AT)katamail.com), May 03 2002; corrected and simplified by Dean Hickerson (dean.hickerson(AT)yahoo.com), Apr 20 2003
Except for n=2, a(n) is the smallest number k > 0 such that 3 divides prime(n)^k - 1. - T. D. Noe (noe(AT)sspectra.com), Apr 17 2003
a(n) <> 0 for n <> 2; a(A049084(A003627(n)))=2; a(A049084(A002476(n)))=1; A134323(n) = (1 - 0^a(n)) * (-1)^(a(n)+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 21 2007
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..10000
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MAPLE
| seq(ithprime(n) mod 3, n=1..105); # Nathaniel Johnston, Jun 29 2011
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MATHEMATICA
| Table[Mod[Prime[n], 3], {n, 10000}]
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CROSSREFS
| Cf. A039702 - A039706, A038194, A007652, A039709 - A039715.
Sequence in context: A178687 A117929 A107455 * A025822 A051585 A049115
Adjacent sequences: A039698 A039699 A039700 * A039702 A039703 A039704
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KEYWORD
| nonn,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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