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A279664 Constant whose Engel Expansion is A007775. 0
1, 1, 5, 6, 9, 0, 5, 1, 5, 3, 7, 5, 4, 0, 2, 8, 9, 5, 4, 5, 0, 1, 3, 4, 5, 8, 1, 5, 5, 7, 2, 3, 2, 1, 4, 6, 5, 3, 5, 2, 5, 5, 4, 0, 2, 8, 9, 4, 8, 7, 9, 5, 3, 6, 4, 7, 0, 0, 3, 9, 9, 3, 8, 9, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This one constant is enough information to uniquely reconstruct A007775.

There appears to be a general expression for higher sets of k-rough numbers.

LINKS

Table of n, a(n) for n=1..66.

B. W. J. Irwin, Constants Whose Engel Expansions are the k-rough Numbers

FORMULA

Define an indexing function over the primes and 7^2.

P(n) = prime(n) for n<16, 49 for n=16, prime(n-1) for n>16.

a = Pi^4*Sum_{k>=0}Sum_{n=1..8} 2^(4-n-8*k)*15^(-n-8*k)/(Prod_{m=1..8} Gamma( P(2+m+n)/30 + k)). - Benedict W. J. Irwin, Dec 16 2016

EXAMPLE

1.15690515375402895450134581557232146535255402894879536470039938959...

MATHEMATICA

Prime7[n_] := If[n < 16, Prime[n], If[n == 16, 7^2, Prime[n - 1]]];

RealDigits[N[Pi^4*Sum[Sum[2^(4-n-8*k)*15^(-n-8*k)/Product[Gamma[ Prime7[2+m+n]/30+k], {m, 1, 8}], {n, 1, 8}], {k, 0, Infinity}], 100]][[1]]

CROSSREFS

Cf. A007775.

Sequence in context: A019149 A172997 A244274 * A230461 A277522 A019598

Adjacent sequences:  A279661 A279662 A279663 * A279665 A279666 A279667

KEYWORD

nonn,cons

AUTHOR

Benedict W. J. Irwin, Dec 16 2016

STATUS

approved

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Last modified January 22 18:53 EST 2019. Contains 319365 sequences. (Running on oeis4.)