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A132822
Decimal expansion of Sum_{n >= 1} 1/7^prime(n).
3
0, 2, 3, 3, 8, 4, 3, 2, 8, 9, 6, 0, 3, 5, 3, 7, 3, 9, 9, 0, 9, 8, 5, 9, 8, 2, 2, 4, 9, 5, 9, 1, 2, 3, 7, 3, 4, 8, 9, 3, 4, 0, 9, 3, 5, 9, 3, 5, 9, 4, 4, 8, 6, 9, 6, 1, 9, 9, 8, 2, 8, 8, 4, 6, 5, 6, 5, 2, 3, 5, 6, 8, 2, 7, 5, 4, 6, 8, 0, 5, 1, 2, 1, 2, 1, 3, 6, 2, 1, 8, 6, 3, 1, 0, 7, 6, 2, 7
OFFSET
0,2
COMMENTS
Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-7 expansion. - M. F. Hasler, Jul 05 2017
FORMULA
From Amiram Eldar, Aug 11 2020: (Start)
Equals Sum_{k>=1} 1/A269327(k).
Equals 6 * Sum_{k>=1} pi(k)/7^(k+1), where pi(k) = A000720(k). (End)
EXAMPLE
0.023384328960353739909859822495912373489340935935944869619982884656523568...
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, 1/7^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 05 2017
CROSSREFS
Cf. A000720, A051006 (analog for base 2), A132800 (analog for base 3), A132806 (analog for base 4), A132797 (analog for base 5), A132817 (analog for base 6), A010051 (characteristic function of the primes), A132799 (base 8), A269327.
Sequence in context: A096714 A078035 A295725 * A347823 A185297 A329803
KEYWORD
cons,nonn
AUTHOR
Cino Hilliard, Nov 17 2007
EXTENSIONS
Offset corrected by R. J. Mathar, Feb 05 2009
Edited by M. F. Hasler, Jul 05 2017
STATUS
approved