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A132800
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Decimal expansion of Sum_{n >= 1} 1/3^prime(n).
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7
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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, 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, 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
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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Equals 2 * Sum_{k>=1} pi(k)/3^(k+1), where pi(k) = A000720(k). (End)
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EXAMPLE
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0.15272690272572247152817541874425912430342364271463298508628837536732...
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MATHEMATICA
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RealDigits[Sum[1/3^Prime[k], {k, 100}], 10, 100][[1]] (* Vincenzo Librandi, Jul 05 2017 *)
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PROG
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(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])", ") ) }
(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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