A345974 Decimal expansion of Sum_{k>=0} Product_{i=1..k} 1/(prime(i)-1).

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

Offset: 1

Author

Hugo Pfoertner, Jun 30 2021

Keywords

• nonn
• cons

Examples

			2.64810175970147102337088414536064714927258700214033932076744547925274...
		

Links

• Peter Cameron, A new constant?, Blog Post, May 23 2021.
• Peter Cameron, A new constant?, local copy of Blog Post, with permission.

Crossrefs

Cf. A005867, A055932, A057335, A345965.

Programs

Maple

c:= sum(product(1/(ithprime(i)-1), i=1..k), k=0..infinity):
evalf(c, 140);  # Alois P. Heinz, Jun 30 2021

PARI

suminf(k=0,prod(i=1,k,1/(prime(i)-1)))

Formula

Equals Sum_{k>=0} 1/A005867(k) = Sum_{k>=1} 1/A055932(k) = Sum_{k>=1} 1/A057335(k). - Amiram Eldar, Jun 26 2025