A088463
Upper twin primes of upper twin prime index.
Original entry on oeis.org
31, 61, 181, 283, 811, 1279, 1999, 2551, 3931, 4159, 5659, 6553, 8389, 9241, 9463, 11551, 12253, 14629, 15889, 17923, 20509, 26113, 27109, 29401, 33829, 37993, 41179, 42571, 44623, 46681, 59671, 61333, 62143, 65449, 67759, 81019, 82009
Offset: 1
A082674
Constant term when a polynomial of degree n is fitted to the lower members of the first n+1 twin prime pairs.
Original entry on oeis.org
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
A 5th-degree polynomial through the 6 points (1, 3), (2, 5), (3, 11), (4, 17), (5, 29), (6, 41) has constant term 41.
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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
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