A082675 Constant term when a polynomial of degree <= n is fitted to the first n+1 upper members of the twin prime pairs.
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
Examples
A 5th degree polynomial through the 6 points (1, 5), (2, 7), (3, 13), (4, 19), (5, 31), (6, 43) has constant term 43.
Links
- Robert Israel, Table of n, a(n) for n = 1..1000
- Cino Hilliard, Sicurvqf.exe
Programs
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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
Extensions
Corrected and extended by R. J. Mathar, Oct 31 2006
Definition edited by Robert Israel, Jun 14 2024