A393777 Decimal expansion of Sum_{k>=1} ((prime(k+1)-1)/A002110(k+1))^2.

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

Offset

0,2

Comments

The asymptotic probability that two positive integers selected independently at random have equal numbers of trailing 0's in their primorial-base representations (A276084).

Links

Table of n, a(n) for n=0..104.

Index entries for sequences related to primorial base.

Example

0.129724116364185814954563943639126194181950527418418...

Prog

(PARI) primorial(n) = prod(k = 1, n, prime(k));
sumpos(k = 1, ((prime(k+1) - 1)/primorial(k+1))^2)

Crossrefs

Cf. A002110, A049345, A276084, A393776.

Sequence in context: A389932 A011070 A230480 * A335605 A308320 A254140

Adjacent sequences: A393774 A393775 A393776 * A393778 A393779 A393780

Keyword

nonn,cons

Author

Amiram Eldar, Feb 27 2026

Status

approved