A334073 Decimal expansion of Sum_{k >= 1} e(k)/2^k, where e(k) = 1 if gpf(k+1) > gpf(k) and 0 otherwise, and gpf(k) is the greatest prime dividing k (A006530).

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

Offset: 0

Author

Amiram Eldar, Apr 13 2020

Keywords

• nonn
• cons

Comments

This constant is irrational (Erdős and Pomerance, 1978).

It is assumed that gpf(1) = A006530(1) = 1.

Examples

			0.83522592242052459434878298057517624119404331710532...
		

Links

• Paul Erdős and Carl Pomerance, On the largest prime factors of n and n + 1, Aequationes mathematicae, Vol. 17, No. 1 (1978), pp. 115-115, alternative link.

Crossrefs

Cf. A006530, A070089.

Programs

Mathematica

gpf[n_] := FactorInteger[n][[-1, 1]]; e[n_] := Boole[gpf[n+1] > gpf[n]]; RealDigits[Sum[e[n]/2^n, {n, 1, 500}], 10, 100][[1]]