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A132797
Decimal expansion of Sum_{n >= 1} 1/5^prime(n).
5
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
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
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
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