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A001576
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1^n + 2^n + 4^n.
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94
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3, 7, 21, 73, 273, 1057, 4161, 16513, 65793, 262657, 1049601, 4196353, 16781313, 67117057, 268451841, 1073774593, 4295032833, 17180000257, 68719738881, 274878431233, 1099512676353, 4398048608257, 17592190238721
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Equals A135576, except for the first member. [From Omar E. Pol (info(AT)polprimos.com), Nov 18 2008]
Conjecture: Let n>1, if a(n)= 1^n+2^n+4^n is a prime number then n is the form 3^h. Example, for h=1, n=3, a(n)= 1^3+2^3+4^3=73 (prime); h=2, n=9, a(n)= 1^9 + 2^9 + 4^9 = 262657 (prime); for h=3, n=27, a(n) is not prime. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 03 2010]
The previous conjecture was proved in 1978. See A051154. [From T. D. Noe (noe(AT)sspectra.com), Aug 15 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
Index entries for sequences related to linear recurrences with constant coefficients, signature (7,-14,8).
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FORMULA
| a(n) = 6*a(n-1) - 8*a(n-2) +3.
O.g.f.: -1/(-1+x)-1/(-1+2*x)-1/(-1+4*x). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 29 2008
E.g.f.: e^x+e^(2*x)+e^(4*x) [From Mohammad K. Azarian (azarian(AT)evansville.edu), Dec 26 2008]
a(n) = A024088(n)/A000225(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 15 2009]
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MATHEMATICA
| Table[1^n + 2^n + 4^n, {n, 0, 24}]
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PROG
| (Other) sage: [sigma(4, n)for n in xrange(0, 23)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
(PARI) a(n)=1+2^n+4^n \\ Charles R Greathouse IV, Jun 10 2011
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CROSSREFS
| Cf. A001550, A034513, A001579, A074501 - A074580. See also comments in A051154.
Cf. A135576, A135577.
Sequence in context: A148678 A148679 A148680 * A169587 A075211 A075212
Adjacent sequences: A001573 A001574 A001575 * A001577 A001578 A001579
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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