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Search: id:A082675
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| A082675 |
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Constant term when a polynomial of degree n is fitted to the first n+1 upper members of the twin prime pairs. |
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+0
2
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| 3, 7, 11, 21, 43, 89, 189, 427, 1043, 2691, 7033, 18017, 44505, 105505, 240269, 527037, 1116025, 2283323, 4509663, 8574253, 15613037, 26989461, 43596475, 63714863, 77517777, 54160585, -87072619, -539390367, -1742001767, -4661299495
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Cino Hilliard, Sicurvqf.exe
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EXAMPLE
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A 5-th degree polynomial through the 6 points (1, 5), (2, 7), (3, 13), (4, 19), (5, 31), (6, 43) has constant term 43.
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MAPLE
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A006512 := proc(n) local i, p ; i := 1 ; p := 0 ; while true do while ithprime(i+1)-ithprime(i) <> 2 do i := i+1 ; od ; p := p+1 ; if p = n then RETURN( ithprime(i+1) ) ; fi ; i := i+1 ; od ; end: A082675 := proc(n) local rhs, co, row, col; rhs := linalg[vector](n+1) ; co := linalg[matrix](n+1, n+1) ; for row from 1 to n+1 do rhs[row] := A006512(row) ; for col from 1 to n+1 do co[row, col] := row^(col-1) ; od ; od ; linalg[linsolve](co, rhs)[1] ; end: for n from 1 to 30 do printf("%d, ", A082675(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2006
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CROSSREFS
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Equals lower-member sequence (A082674) + 2.
Cf. A082594.
Sequence in context: A151923 A067498 A018345 this_sequence A028831 A137516 A111668
Adjacent sequences: A082672 A082673 A082674 this_sequence A082676 A082677 A082678
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KEYWORD
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easy,sign
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), May 19 2003
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2006
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