A082674 Constant term when a polynomial of degree n is fitted to the lower members of the first n+1 twin prime pairs.
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
Offset: 1
Examples
A 5th-degree polynomial through the 6 points (1, 3), (2, 5), (3, 11), (4, 17), (5, 29), (6, 41) has constant term 41.
Programs
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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, Oct 31 2006
Formula
a(n) = A082675(n) - 2.
Extensions
Corrected and extended by R. J. Mathar, Oct 31 2006