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 A132817 Decimal expansion of Sum_{n >= 1} 1/6^prime(n). 3
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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 A070151 A331847 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

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Last modified October 27 17:25 EDT 2020. Contains 338035 sequences. (Running on oeis4.)