A225755 - OEIS

%I #34 Jan 05 2025 19:51:40

%S 2,3,6,7,8,7,5,3,1,9,8,0,7,7,0,9,6,0,5,0,3,3,5,0,2,1,1,7,7,0,0,7,9,3,

%T 8,4,8,8,8,1,0,2,5,5,2,0,7,9,0,4,5,0,4,9,9,8,8,8,7,8,0,1,7,2,0,6,9,9,

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

%N Decimal expansion of the constant obtained through Lüroth retro-expansion of the prime sequence.

%H Paolo P. Lava, <a href="/A225755/b225755.txt">Table of n, a(n) for n = 1..1000</a>

%H Arnold Knopfmacher and John Knopfmacher, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/27-1/knopfmacher.pdf">Representations for real numbers via k-th powers of integers</a>, University of Witwatersrand, Johannesburg, South Africa 2050, February 1987.

%e n=2+1/3+1/[(3-1)*3*5]+1/[(3-1)*3*(5-1)*5*7]+... = 2.3678753198077096050335021177007938488810255207904504998...

%p with(numtheory); A225755:=proc(q) local a,b,n;

%p b:=3; a:=2+1/b; for n from 3 to q do

%p b:=b*(ithprime(n-1)-1)*ithprime(n); a:=a+1/b;

%p od; print(evalf(a,2000)); end: A225755(10^4);

%Y Cf. A064648, A132120.

%K nonn,cons

%O 1,1

%A _Paolo P. Lava_, May 28 2013