A165132 Primes whose logarithms are known to possess ternary BBP formulas.

2, 3, 5, 7, 11, 13

Offset: 1

Author

Jaume Oliver Lafont, Sep 04 2009

Keywords

• nonn
• more

Comments

From Jaume Oliver Lafont, 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 link for the definition of P notation.

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

(End)

Links

• David H. Bailey, A Compendium of BBP-formulas for mathematical constants. See p. 24.

Crossrefs

Cf. A104885.

Programs

PARI

\\ Jaume Oliver Lafont, Oct 07 2009
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)