A339766 Decimal expansion of Sum_{n>=1} A054541(n)/A076954(n-1).

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

Offset: 1

Author

Davide Rotondo, Dec 16 2020

Keywords

• nonn
• cons

Comments

With this constant f(1) and using the formula f(n+1) = (floor(f(n))*(f(n))) - ((floor(f(n)))^2 - floor(f(n))) it is possible to obtain the prime numbers repeated exactly a number of times corresponding to the position of the prime number. That is, 2 once, 3 twice, 5 thrice, etc.

Examples

			2.61200074043...
		

Crossrefs

Cf. A054541, A076954, A005145, A249270.

Programs

Mathematica

imax:=87;First[RealDigits[N[2+Sum[(Prime[i]-Prime[i-1])/Product[Prime[j-1]^(j-1),{j,2,i}],{i,2,imax}],imax]]] (* Stefano Spezia, Dec 16 2020 *)

Formula

Equals 2 + (3-2)/(2) + (5-3)/(2*3^2) + (7-5)/(2*3^2*5^3) + (11-7)/(2*3^2*5^3*7^4) + ...