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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)*(p(n)*(p(n)-2)) / gcd( a(n-1)*p(n)*(p(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

CROSSREFS

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 September 19 02:20 EDT 2021. Contains 347550 sequences. (Running on oeis4.)