1,1

Contribution from Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 07 2009: (Start)

log(2)=(2/3)P(1,9,2,(1,0))

log(3)=(1/9)P(1,9,2,(9,1))

log(5)=(4/27)P(1,3^4,4,(9,3,1,0))

log(7)=(1/3^5)P(1,3^6,6,(405,81,72,9,5,0))

log(11)=(1/(2*3^9))P(1,3^10,10,(85293,10935,9477,1215,648,135,117,15,13,0))

log(13)=(1/3^5)P(1,3^6,6,(567,81,36,9,7,0))

See the reference for the definition of P notation.

Equivalent expressions in reduced coefficients are given in the code section.

(End)

David H. Bailey, A Compendium of BBP-formulas for mathematical constants [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 07 2009]

Contribution from Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 07 2009: (Start)

(PARI) log2=2*suminf(k=1, [0, 1][k%2+1]/k/3^k)

log3=suminf(k=1, [1, 3][k%2+1]/k/3^k)

log5=4*suminf(k=1, [0, 1, 1, 1][k%4+1]/k/3^k)

log7=suminf(k=1, [0, 5, 3, 8, 3, 5][k%6+1]/k/3^k)

log11=suminf(k=1, [0, 13, 5, 13, 5, 8, 5, 13, 5, 13][k%10+1]/k/3^k)/2

log13=suminf(k=1, [0, 7, 3, 4, 3, 7][k%6+1]/k/3^k)

(End)

Cf. A104885.

Sequence in context: A028834 A139750 A139749 this_sequence A039715 A039714 A039713

Adjacent sequences: A165129 A165130 A165131 this_sequence A165133 A165134 A165135

more,nonn

Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 04 2009