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A047241
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Numbers that are congruent to {1, 3} mod 6.
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13
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1, 3, 7, 9, 13, 15, 19, 21, 25, 27, 31, 33, 37, 39, 43, 45, 49, 51, 55, 57, 61, 63, 67, 69, 73, 75, 79, 81, 85, 87, 91, 93, 97, 99, 103, 105, 109, 111, 115, 117, 121, 123, 127, 129, 133, 135, 139, 141, 145, 147, 151, 153, 157, 159, 163, 165, 169, 171, 175, 177, 181
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also the numbers n such that 10^p+k could possibly be prime. - Roderick MacPhee, Nov 20 2011
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FORMULA
| G.f.: (1+2x+3x^2)/((1+x)(1-x)^2)=(1+2x+3x^2)/((1-x)(1-x^2)); E.g.f.: (6x+1)exp(x)/2+exp(-x)/2; a(n)=3n-5/2-(-1)^n/2. - Paul Barry (pbarry(AT)wit.ie), Sep 04 2003
a(n) = 2*floor((n-1)/2) + 2*n -1 [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 18 2010]
a(n)=6*n-a(n-1)-8 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 05 2010]
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EXAMPLE
| For n=2. a(2)=6*2-1-8=3; n=3, a(3)=6*3-3-8=7; n=4, a(4)=6*4-7-8=9 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 05 2010]
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CROSSREFS
| Cf. A047233. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Jun 24 2010]
Subsequence of A186422.
Sequence in context: A087064 A189561 A087550 * A086515 A132222 A111225
Adjacent sequences: A047238 A047239 A047240 * A047242 A047243 A047244
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
Corrected formula by Bruno Berselli (berselli.bruno(AT)yahoo.it), Jun 24 2010
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