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A132817
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Decimal expansion of Sum_{n >= 1} 1/6^prime(n).
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4
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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
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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-6 expansion. - M. F. Hasler, Jul 05 2017
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1110
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FORMULA
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Equals 5 * Sum_{k>=1} pi(k)/6^(k+1), where pi(k) = A000720(k). - Amiram Eldar, Aug 11 2020
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EXAMPLE
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0.032539583308525544049260050781274181192986076617578098887664610099...
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MATHEMATICA
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Join[{0}, RealDigits[FromDigits[{{Table[If[PrimeQ[n], 1, 0], {n, 370}]}, 0}, 6], 10, 111][[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, 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
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CROSSREFS
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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
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KEYWORD
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cons,nonn
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AUTHOR
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Cino Hilliard, Nov 17 2007
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EXTENSIONS
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Offset corrected R. J. Mathar, Jan 26 2009
Edited by M. F. Hasler, Jul 05 2017
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STATUS
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approved
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