The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A377010

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

Decimal expansion of the asymptotic mean of A376928: lim_{m->oo} (1/m) * Sum_{k=1..m} A376928(k).
(history; published version)

#6 by N. J. A. Sloane at Sun Oct 13 11:17:30 EDT 2024

STATUS

proposed

approved

#5 by Amiram Eldar at Sat Oct 12 15:46:20 EDT 2024

STATUS

editing

proposed

#4 by Amiram Eldar at Sat Oct 12 15:45:11 EDT 2024

PROG

(PARI) \p 200120

#3 by Amiram Eldar at Sat Oct 12 15:44:58 EDT 2024

PROG

(PARI) \p 200

#2 by Amiram Eldar at Sat Oct 12 15:43:53 EDT 2024

NAME

allocated for Amiram Eldar

Decimal expansion of the asymptotic mean of A376928: lim_{m->oo} (1/m) * Sum_{k=1..m} A376928(k).

DATA

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

OFFSET

1,2

FORMULA

Equals 1/2 + Sum_{p prime} p * (1/p# - 1/nextprime(p)#), where nextprime(p) = A151800(p) and p# = A034386(p).

Equals 1/2 + Sum_{k>=1} prime(k) * (1/A002110(k) - 1/A002110(k+1)).

EXAMPLE

1.74466340501740192345730888352581703598570050436409...

PROG

(PARI)\p 200

f(k) = prod(i = 1, k, prime(i));

1/2 + suminf(k = 1, prime(k) * (1/f(k) - 1/f(k+1)))

CROSSREFS

Cf. A002110, A034386, A151800, A249270, A376928.

KEYWORD

allocated

nonn,cons

AUTHOR

Amiram Eldar, Oct 12 2024

STATUS

approved

editing

#1 by Amiram Eldar at Sat Oct 12 15:43:53 EDT 2024

NAME

allocated for Amiram Eldar

KEYWORD

allocated

STATUS

approved