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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

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

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

STATUS

approved

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Last modified October 16 20:36 EDT 2021. Contains 348047 sequences. (Running on oeis4.)