A334073 - OEIS

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).

%I #4 Apr 13 2020 19:49:40

%S 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,

%T 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,

%U 0,3,1,8,5,7,9,4,0,5,1,0,5,3,3,8,3,3,5

%N 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).

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

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

%H Paul Erdős and Carl Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/PDF/paper17.pdf">On the largest prime factors of n and n + 1</a>, Aequationes mathematicae, Vol. 17, No. 1 (1978), pp. 115-115, <a href="https://www.renyi.hu/~p_erdos/1978-29.pdf">alternative link</a>.

%e 0.83522592242052459434878298057517624119404331710532...

%t 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]]

%Y Cf. A006530, A070089.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Apr 13 2020