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A082674
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Constant term when a polynomial of degree n is fitted to the first n+1 lower members of the twin prime pairs.
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2
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1, 5, 9, 19, 41, 87, 187, 425, 1041, 2689, 7031, 18015, 44503, 105503, 240267, 527035, 1116023, 2283321, 4509661, 8574251, 15613035, 26989459, 43596473, 63714861, 77517775, 54160583, -87072621, -539390369, -1742001769, -4661299497
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Cino Hilliard, Sicurvqf.exe
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FORMULA
| Equals upper-member sequence (A082675(n)) - 2.
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EXAMPLE
| A 5-th degree polynomial through the 6 points (1, 3), (2, 5), (3, 11), (4, 13), (5, 17), (6, 29) has constant term 41.
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MAPLE
| A088460 := 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) ) ; fi ; i := i+1 ; od ; end: A082674 := 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] := A088460(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, ", A082674(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2006
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CROSSREFS
| Cf. A082594, A082675.
Sequence in context: A160722 A061202 A060161 * A102172 A011983 A087940
Adjacent sequences: A082671 A082672 A082673 * A082675 A082676 A082677
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KEYWORD
| easy,sign
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), May 19 2003
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EXTENSIONS
| Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2006
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