A279664 Constant whose Engel Expansion is A007775.

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

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