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A132806
Decimal expansion of Sum_{n >= 1} 1/4^prime(n).
4
0, 7, 9, 1, 6, 2, 8, 5, 1, 0, 3, 7, 8, 5, 0, 1, 4, 9, 6, 7, 1, 7, 7, 1, 1, 1, 7, 9, 6, 2, 2, 0, 8, 1, 8, 4, 6, 1, 3, 0, 3, 8, 5, 6, 9, 7, 5, 1, 8, 7, 8, 0, 8, 4, 1, 7, 9, 0, 9, 9, 9, 1, 5, 2, 3, 1, 2, 0, 9, 6, 3, 2, 6, 6, 1, 3, 8, 1, 7, 1, 1, 5, 8, 2, 7, 8, 0, 6, 7, 0, 3, 6, 0, 2, 2, 2, 0, 6
OFFSET
0,2
COMMENTS
Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-4 expansion. - M. F. Hasler, Jul 04 2017
FORMULA
Equals 3 * Sum_{k>=1} pi(k)/4^(k+1), where pi(k) = A000720(k). - Amiram Eldar, Aug 11 2020
EXAMPLE
0.079162851037850149671771117962208184613038569751878...
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, 1/4^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), A132797 (analog for base 5), A010051 (characteristic function of the primes), A000040 (the primes).
Sequence in context: A086318 A244674 A130834 * A016629 A154203 A375189
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