A132800 - OEIS

%I #24 Aug 11 2020 09:59:34

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

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

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

%N Decimal expansion of Sum_{n >= 1} 1/3^prime(n).

%C Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-3 expansion. - _M. F. Hasler_, Jul 04 2017.

%H Vincenzo Librandi, <a href="/A132800/b132800.txt">Table of n, a(n) for n = 0..2000</a>

%F From _Amiram Eldar_, Aug 11 2020: (Start)

%F Equals Sum_{k>=1} 1/A057901(k).

%F Equals 2 * Sum_{k>=1} pi(k)/3^(k+1), where pi(k) = A000720(k). (End)

%e 0.15272690272572247152817541874425912430342364271463298508628837536732...

%t RealDigits[Sum[1/3^Prime[k], {k, 100}], 10, 100][[1]] (* _Vincenzo Librandi_, Jul 05 2017 *)

%o (PARI) /* Sum of 1/m^p for primes p */ sumnp(n,m) = { local(s=0,a,j); for(x=1,n, s+=1./m^prime(x); ); a=Vec(Str(s)); for(j=3,100, print1(eval(a[j])",") ) }

%o (PARI) suminf(n=1,1/3^prime(n)) \\ Then: digits(%\.1^default(realprecision))[1..-3] to remove the last 2 digits. N.B.: Functions sumpos() and sumnum() yield much less accurate results. - _M. F. Hasler_, Jul 04 2017

%Y Cf. A000720, A051006 (analog for base 2), A132797 (analog for base 5), A010051 (characteristic function of the primes), A057901, A132806 (base 4).

%K cons,nonn

%O 0,2

%A _Cino Hilliard_, Nov 17 2007

%E Offset corrected _R. J. Mathar_, Jan 26 2009

%E Edited by _M. F. Hasler_, Jul 04 2017