OFFSET
1,1
COMMENTS
Smallest distance (A052380) and also smallest possible increment of twin-distances is 6.
Primes may occur between p+2 and p+6n.
LINKS
Norman Luhn, Table of n, a(n) for n = 1..4624 (terms 1..4500 from Martin Raab).
FORMULA
The prime a(n) determines a prime quadruple: [p, p+2, p+6n, p+6n+2] and a [2, 6n-2, 2] d-pattern.
EXAMPLE
The first 3 terms (5, 17, 41) are followed by difference patterns as it is displayed: 5 by [2, 4, 2], 17 by [2, 4+6, 2], 41 by [2, 4+6+6, 2] determining prime quadruples: (5, 7, 11, 13), (17, 19, 29, 31) or (41, 43, 59, 61), respectively.
a(10)=461 gives the quadruple [461, 463, 521=461+60, 523], and between 521 and 463, 7 primes occur.
MATHEMATICA
NextLowerTwinPrim[n_] := Block[{k = n + 6}, While[ !PrimeQ[k] || !PrimeQ[k + 2], k += 6]; k]; p = 5; t = Table[0, {50}]; Do[ q = NextLowerTwinPrim[p]; d = (q - p)/6; If[d < 51 && t[[d]] == 0, t[[d]] = p; Print[{d, p}]]; p = q, {n, 1500}]; t (* Robert G. Wilson v, Oct 28 2005 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 07 2000
STATUS
approved