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

%I A165132 #13 Jul 22 2025 07:20:11
%S A165132 2,3,5,7,11,13
%N A165132 Primes whose logarithms are known to possess ternary BBP formulas.
%C A165132 From _Jaume Oliver Lafont_, Oct 07 2009: (Start)
%C A165132 log(2)=(2/3)P(1,9,2,(1,0))
%C A165132 log(3)=(1/9)P(1,9,2,(9,1))
%C A165132 log(5)=(4/27)P(1,3^4,4,(9,3,1,0))
%C A165132 log(7)=(1/3^5)P(1,3^6,6,(405,81,72,9,5,0))
%C A165132 log(11)=(1/(2*3^9))P(1,3^10,10,(85293,10935,9477,1215,648,135,117,15,13,0))
%C A165132 log(13)=(1/3^5)P(1,3^6,6,(567,81,36,9,7,0))
%C A165132 See the link for the definition of P notation.
%C A165132 Equivalent expressions in reduced coefficients are given in the code section.
%C A165132 (End)
%H A165132 David H. Bailey, <a href="https://www.davidhbailey.com/dhbpapers/bbp-formulas.pdf">A Compendium of BBP-formulas for mathematical constants</a>. See p. 24.
%o A165132 (PARI) \\ _Jaume Oliver Lafont_, Oct 07 2009
%o A165132 log2=2*suminf(k=1,[0,1][k%2+1]/k/3^k)
%o A165132 log3=suminf(k=1,[1,3][k%2+1]/k/3^k)
%o A165132 log5=4*suminf(k=1,[0,1,1,1][k%4+1]/k/3^k)
%o A165132 log7=suminf(k=1,[0,5,3,8,3,5][k%6+1]/k/3^k)
%o A165132 log11=suminf(k=1,[0,13,5,13,5,8,5,13,5,13][k%10+1]/k/3^k)/2
%o A165132 log13=suminf(k=1,[0,7,3,4,3,7][k%6+1]/k/3^k)
%Y A165132 Cf. A104885.
%K A165132 nonn,more
%O A165132 1,1
%A A165132 _Jaume Oliver Lafont_, Sep 04 2009