login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132817 Decimal expansion of Sum_{n >= 1} 1/6^prime(n). 3
0, 3, 2, 5, 3, 9, 5, 8, 3, 3, 0, 8, 5, 2, 5, 5, 4, 4, 0, 4, 9, 2, 6, 0, 0, 5, 0, 7, 8, 1, 2, 7, 4, 1, 8, 1, 1, 9, 2, 9, 8, 6, 0, 7, 6, 6, 1, 7, 5, 7, 8, 0, 9, 8, 8, 8, 7, 6, 6, 4, 6, 1, 0, 0, 9, 9, 0, 7, 6, 7, 7, 3, 8, 3, 1, 3, 0, 3, 9, 1, 5, 1, 6, 3, 3, 8, 8, 0, 9, 3, 4, 8, 0, 6, 3, 5, 4, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-6 expansion. - M. F. Hasler, Jul 05 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1110

FORMULA

Equals 5 * Sum_{k>=1} pi(k)/6^(k+1), where pi(k) = A000720(k). - Amiram Eldar, Aug 11 2020

EXAMPLE

0.032539583308525544049260050781274181192986076617578098887664610099...

MATHEMATICA

Join[{0}, RealDigits[FromDigits[{{Table[If[PrimeQ[n], 1, 0], {n, 370}]}, 0}, 6], 10, 111][[1]]] (* Vincenzo Librandi, Jul 05 2017 *)

PROG

(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, n, print1(eval(a[j])", ") ) }

(PARI) suminf(n=1, 1/6^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

CROSSREFS

Cf. A000720, A051006 (analog for base 2), A132800 (analog for base 3), A132806 (analog for base 4), A132797 (analog for base 5), A132822 (analog for base 7), A010051 (characteristic function of the primes), A000040 (the primes).

Sequence in context: A238628 A045766 A281668 * A131025 A070151 A331847

Adjacent sequences:  A132814 A132815 A132816 * A132818 A132819 A132820

KEYWORD

cons,nonn

AUTHOR

Cino Hilliard, Nov 17 2007

EXTENSIONS

Offset corrected R. J. Mathar, Jan 26 2009

Edited by M. F. Hasler, Jul 05 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 27 17:25 EDT 2020. Contains 338035 sequences. (Running on oeis4.)