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

1,2

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = A082675(n) - 2.

Example

A 5th-degree polynomial through the 6 points (1, 3), (2, 5), (3, 11), (4, 17), (5, 29), (6, 41) has constant term 41.

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

Crossrefs

Cf. A001359, A082594, A082675.

Sequence in context: A295966 A060161 A282730 * A292773 A228338 A309731

Adjacent sequences: A082671 A082672 A082673 * A082675 A082676 A082677

Keyword

easy,sign

Author

Cino Hilliard, May 19 2003

Extensions

Corrected and extended by R. J. Mathar, Oct 31 2006

Status

approved