login
A082675
Constant term when a polynomial of degree <= n is fitted to the first n+1 upper members of the twin prime pairs.
2
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
OFFSET
1,1
LINKS
Cino Hilliard, Sicurvqf.exe
EXAMPLE
A 5th degree polynomial through the 6 points (1, 5), (2, 7), (3, 13), (4, 19), (5, 31), (6, 43) has constant term 43.
MAPLE
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, Oct 31 2006
CROSSREFS
Equals lower-member sequence (A082674) + 2.
Cf. A082594.
Sequence in context: A187264 A067498 A018345 * A201645 A028831 A244572
KEYWORD
easy,sign
AUTHOR
Cino Hilliard, May 19 2003
EXTENSIONS
Corrected and extended by R. J. Mathar, Oct 31 2006
Definition edited by Robert Israel, Jun 14 2024
STATUS
approved