A380741 Decimal expansion of Sum_{k>=1} prime(k)/2^(k!).

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

Offset

1,2

Comments

Each prime can be recovered from this constant r by prime(k) = floor(r*2^(k!) - floor(r*2^((k-1)!)))*2^((k-1)*(k-1)!) when the binary positions 2^(k!) are far enough apart, which means k>=3.

Is this constant transcendental?

Links

Table of n, a(n) for n=1..105.

Example

1.828125417232513427734375...

Prog

(PARI) suminf(k=1, prime(k)/2^(k!)) \\ Michel Marcus, Feb 09 2025

Crossrefs

Cf. A339764.

Sequence in context: A248299 A393895 A253721 * A021551 A143025 A303326

Adjacent sequences: A380738 A380739 A380740 * A380742 A380743 A380744

Keyword

nonn,cons,easy

Author

Davide Rotondo, Jan 31 2025

Extensions

More terms from Amiram Eldar, Jan 31 2025

Status

approved