A341930 Decimal expansion of (A249270 + A340469)/2.

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

Offset: 1

Author

Davide Rotondo, Feb 23 2021

Keywords

• nonn
• cons

Comments

With this constant r(1) and using the formula r(n+1) = round(r(n))*(r(n) - round(r(n)) + 1.5) it is possible to obtain the sequence of prime numbers because round(r(n)) = prime(n).

Examples

			2.06743589142023422951884707566789...
		

Crossrefs

Cf. A249270, A340469.

Programs

PARI

suminf(k=1, (prime(k)-1.5)/prod(i=1, k-1, prime(i))) \\ Michel Marcus, Feb 23 2021

Formula

r(1) = Sum_{k>=1} (prime(k)-1.5)/Product_{i=1..k-1} prime(i).