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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..1000 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 Adjacent sequences: A082672 A082673 A082674 * A082676 A082677 A082678 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

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Last modified August 11 17:54 EDT 2024. Contains 375073 sequences. (Running on oeis4.)