A132817 - OEIS

A132817

Decimal expansion of Sum_{n >= 1} 1/6^prime(n).

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

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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 A340702 A070151

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