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 A062270 Numerators in partial products of the twin prime constant. 7
 3, 45, 175, 693, 11011, 2807805, 302307005, 402243205, 714186915, 42803602439, 11086133031701, 5908908905896633, 1488200914442251997, 3041106216468949733, 16213234917387714257, 21611220383343195817 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS For n>1, a(n) is the absolute value of the numerator of the determinant of the n X n matrix with elements M[i,j] = 1/(prime(i)-1)^2 for i=j and 1 otherwise. - Alexander Adamchuk, Jun 02 2006 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 84-94. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, ch. 22.20 LINKS Table of n, a(n) for n=2..17. Steven R. Finch, Hardy-Littlewood Constants [Broken link] Steven R. Finch, Hardy-Littlewood Constants [From the Wayback machine] FORMULA a(n) = a(n-1)*(prime(n)*(prime(n)-2)) / gcd(a(n-1)*prime(n)*(prime(n)-2), A062271(n)) for n > 2. EXAMPLE a(4) = 175 = 3*1*5*3*7*5 / gcd(3*1*5*3*7*5, 2*2*4*4*6*6). MATHEMATICA Numerator[Abs[Table[ Det[ DiagonalMatrix[ Table[ 1/(Prime[i]-1)^2 - 1, {i, 1, n} ] ] + 1 ], {n, 2, 20} ]]] (* Alexander Adamchuk, Jun 02 2006 *) PROG (PARI) a(n) = numerator(prod(k=2, n, 1-1/(prime(k)-1)^2)); \\ Michel Marcus, May 31 2022 CROSSREFS Cf. A062271 (denominators), A005597 (decimal expansion). Sequence in context: A071968 A170921 A093585 * A069955 A289193 A062346 Adjacent sequences: A062267 A062268 A062269 * A062271 A062272 A062273 KEYWORD easy,nonn,frac AUTHOR Frank Ellermann, Jun 16 2001 EXTENSIONS Typo in link corrected by Martin Griffiths, Apr 03 2009 STATUS approved

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Last modified June 2 22:56 EDT 2023. Contains 363102 sequences. (Running on oeis4.)