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A262153 Decimal expansion of Sum_{p prime} 1/(2^p-1), a prime equivalent of the Erdős-Borwein constant. 0
5, 1, 6, 9, 4, 2, 8, 1, 9, 8, 0, 5, 6, 4, 0, 3, 8, 4, 2, 4, 0, 5, 1, 6, 6, 0, 8, 4, 7, 9, 8, 5, 6, 2, 7, 7, 9, 7, 8, 5, 4, 6, 9, 4, 7, 9, 1, 3, 0, 9, 1, 2, 4, 1, 6, 5, 0, 2, 8, 0, 2, 4, 5, 8, 7, 1, 2, 3, 8, 0, 7, 5, 3, 4, 1, 1, 3, 6, 0, 3, 7, 7, 1, 9, 8, 1, 8, 0, 2, 8, 0, 5, 4, 0, 2, 5, 0, 8, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Erdős was interested in the question whether this constant is irrational. - Amiram Eldar, Apr 30 2020

REFERENCES

Paul Erdős, Some of my favourite unsolved problems, in A. Baker, B. Bollobás and A. Hajnal (eds.), A Tribute to Paul Erdős, Cambridge University Press, 1990, p. 470.

LINKS

Table of n, a(n) for n=0..99.

Paul Erdős, On arithmetical properties of Lambert series, J. Indian Math. Soc. (N.S.), Vol. 12 (1948), pp. 63-66.

Paul Erdős, On the irrationality of certain series, Math. Student, Vol. 36 (1969), pp. 222-226.

Eric Weisstein's World of Mathematics, Erdős-Borwein Constant.

Eric Weisstein's World of Mathematics, Prime Constant.

FORMULA

Equals Sum_{i>=1} 1/A001348(i). - R. J. Mathar, Feb 17 2016

Equals Sum_{k>=1} omega(k)/2^k, where omega(k) is the number of distinct primes dividing k (A001221). - Amiram Eldar, Apr 30 2020

EXAMPLE

0.51694281980564038424051660847985627797854694791309124165028...

MATHEMATICA

digits = 100; m0 = 100; dm = 100; s[m_] := s[m] = N[Sum[1/(2^Prime[n]-1), {n, 1, m}], digits+10]; s[m = m0]; Print[{m, s[m]}]; s[m = m + dm]; While[ Print[{m, s[m]}]; RealDigits[ s[m], 10, digits+5] != RealDigits[ s[m - dm], 10, digits+5], m = m + dm]; RealDigits[ s[m], 10, digits] // First

PROG

(PARI) suminf(k=1, omega(k)/2^k) \\ Michel Marcus, Apr 30 2020

CROSSREFS

Cf. A051006, A065442.

Sequence in context: A306700 A058651 A164105 * A160824 A193586 A007397

Adjacent sequences:  A262150 A262151 A262152 * A262154 A262155 A262156

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Sep 13 2015

STATUS

approved

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Last modified May 29 04:33 EDT 2020. Contains 334697 sequences. (Running on oeis4.)