0,2

For prime p, p divides a(p-1). [From T. D. Noe (noe(AT)sspectra.com), Apr 11 2009]

D. Jarden, Recurring Sequences. Riveon Lematematika, Jerusalem, 1966.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. W. Wrench, Jr., Evaluation of Artin's constant and the twin-prime constant, Math. Comp., 15 (1961), 396-398.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

a(n) = A000204(n)-1 = A000032(n+1)-1 = A000071(n+1)+A000045(n)

a(n)=F(n)+F(n+2)-1 {where F(n) is the n-th Fibonacci number} - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008

a(n) = A014217(n+1)- A000035(n+1). - Paul Curtz (bpcrtz(AT)free.fr), Sep 21 2008

a(n)=-1+(1/2)*[1/2+(1/2)*sqrt(5)]^n+(1/2)*[1/2+(1/2)*sqrt(5)]^n*sqrt(5)-(1/2)*sqrt(5)*[1/2-(1/2) *sqrt(5)]^n+(1/2)*[1/2-(1/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Sep 29 2008]

A001610:=-z*(-2+z)/(z-1)/(z**2+z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

with(combinat): seq(fibonacci(n)+fibonacci(n+2)-1, n=0..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008

g:=(1+z^2)/(1-z-z^2): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)-1, n=1..37); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]

Cf. A001610, A000032, A000204.

Sequence in context: A026647 A026669 A023614 this_sequence A135431 A123908 A026397

Adjacent sequences: A001607 A001608 A001609 this_sequence A001611 A001612 A001613

nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Henry Bottomley (se16(AT)btinternet.com), Jul 06 2000