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%I #19 Jun 14 2024 10:06:47
%S 3,7,11,21,43,89,189,427,1043,2691,7033,18017,44505,105505,240269,
%T 527037,1116025,2283323,4509663,8574253,15613037,26989461,43596475,
%U 63714863,77517777,54160585,-87072619,-539390367,-1742001767,-4661299495
%N Constant term when a polynomial of degree <= n is fitted to the first n+1 upper members of the twin prime pairs.
%H Robert Israel, <a href="/A082675/b082675.txt">Table of n, a(n) for n = 1..1000</a>
%H Cino Hilliard, <a href="http://groups.msn.com/BC2LCC/page.msnw?fc_p=%2FSicurv%20%2D%20Simul%20Equ%20and%20Curve%20Fitting&fc_a=0">Sicurvqf.exe</a>
%e A 5th degree polynomial through the 6 points (1, 5), (2, 7), (3, 13), (4, 19), (5, 31), (6, 43) has constant term 43.
%p 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
%Y Equals lower-member sequence (A082674) + 2.
%Y Cf. A082594.
%K easy,sign
%O 1,1
%A _Cino Hilliard_, May 19 2003
%E Corrected and extended by _R. J. Mathar_, Oct 31 2006
%E Definition edited by _Robert Israel_, Jun 14 2024