A132797 - OEIS

A132797

Decimal expansion of Sum_{n >= 1} 1/5^prime(n).

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

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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-5 expansion. - M. F. Hasler, Jul 04 2017

LINKS

Table of n, a(n) for n=0..97.

FORMULA

From Amiram Eldar, Aug 11 2020: (Start)

Equals Sum_{k>=1} 1/A057902(k).

Equals 4 * Sum_{k>=1} pi(k)/5^(k+1), where pi(k) = A000720(k). (End)

EXAMPLE

0.0483328213005632326916634712515665965227023410340158272294967746839279...

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, 1/5^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), A057902, A132800 (analog for base 3), A132806 (analog for base 4), A010051 (characteristic function of the primes), A132817 (base 6).

Sequence in context: A332905 A021211 A019698 * A309217 A217602 A300690

Adjacent sequences: A132794 A132795 A132796 * A132798 A132799 A132800

KEYWORD

cons,nonn

AUTHOR

Cino Hilliard, Nov 17 2007

EXTENSIONS

Offset corrected R. J. Mathar, Jan 26 2009

Edited by M. F. Hasler, Jul 04 2017

STATUS

approved