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

0,1

Comments

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

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

Links

Table of n, a(n) for n=0..86.

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.

Example

0.83522592242052459434878298057517624119404331710532...

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]]

Crossrefs

Cf. A006530, A070089.

Sequence in context: A199293 A357108 A110234 * A196654 A019728 A265183

Adjacent sequences: A334070 A334071 A334072 * A334074 A334075 A334076

Keyword

nonn,cons

Author

Amiram Eldar, Apr 13 2020

Status

approved