A323828 Decimal expansion of a constant related to Bertrand's Postulate.

3, 5, 6, 7, 9, 7, 6, 0, 9, 0, 9, 8, 4, 6, 6, 3, 4, 6, 1, 2, 3, 6, 6, 0, 0, 7, 7, 3, 7, 1, 9, 2, 5, 2, 6, 4, 2, 5, 5, 2, 7, 9, 4, 3, 0, 2, 8, 9, 7, 7, 9, 1, 3, 3, 1, 1, 1, 7, 0, 1, 1, 6, 6, 8, 8, 9, 8, 9, 1, 9, 3, 0, 9, 2, 0, 0, 5, 1, 4, 6, 0, 2, 5, 8, 3, 4, 2, 9, 4, 0, 7, 4, 1, 6, 0, 4, 9, 4, 7, 7, 7, 5

Offset

1,1

Links

Table of n, a(n) for n=1..102.

Dylan Fridman et al., A prime-representing constant, Amer. Math. Monthly 126 (2019), 72-73 (on ResearchGate).

Formula

Sum_{k>=1} (2^(k-1) + 1)/(Product_{i=1..k-1} 2^(i-1) + 2). See Dylan Fridman et al. reference. - Freddy Barrera, Feb 17 2019

Example

3.5679760909846634612366007737192526425527943028977913311170116688989193092...

Maple

evalf(Sum((2^(k-1) + 1)/Product(2^(i-1) + 2, i=1..k-1), k=1..infinity), 120); # Vaclav Kotesovec, Jun 04 2019

Prog

(Sage)
def g(n):
    return sum((2^(k-1) + 1)/prod(2^(i-1) + 2 for i in (1..k-1))
               for k in (1..n))
N(g(100), digits=102) # Freddy Barrera, Feb 17 2019

Crossrefs

Cf. A249720, A051254.

Sequence in context: A010906 A114309 A324060 * A079581 A229858 A269020

Adjacent sequences: A323825 A323826 A323827 * A323829 A323830 A323831

Keyword

nonn,cons

Author

N. J. A. Sloane, Feb 01 2019

Extensions

More terms from Freddy Barrera, Feb 17 2019

Status

approved