%I A085580
%S A085580 6,3,1,4,0,3,1,8,3,0,3,5,2,7,6,7,4,7,9,3,0,8,9,4,2,4,1,2,1,0,7,7,7,1,2,
%T A085580 2,4,6,0,4,6,5,7,3,5,5,7,6,6,0,7,7,7,3,8,9,5,8,4,0,3,3,1,7,7,5,5,6,9,6,
%U A085580 6,1,2,3,7,9,7,5,9,9,3,4,5,7,7,2,9,5,0,1,6,5,5,4,1,4,6,2,2,6
%N A085580 a(n) = (n+1)-st digit after decimal point of d, where d = (sqrt((n+1)^2 
               + 4(n+1)) - (n+1))/2.
%e A085580 ===============================================================
%e A085580 n ... n+1 ... a(n) ... Value of d with first n+1 decimals only
%e A085580 ===============================================================
%e A085580 0 ... 1 ...... 6 ..... 0.6
%e A085580 1 ... 2 ...... 3 ..... 0.73
%e A085580 2 ... 3 ...... 1 ..... 0.791
%e A085580 3 ... 4 ...... 4 ..... 0.8284
%e A085580 4 ... 5 ...... 0 ..... 0.85410
%e A085580 5 ... 6 ...... 3 ..... 0.872983
%e A085580 6 ... 7 ...... 1 ..... 0.8874821
%e A085580 7 ... 8 ...... 8 ..... 0.89897948
%e A085580 8 ... 9 ...... 3 ..... 0.908326913
%e A085580 9 ... 10 ..... 0 ..... 0.9160797830
%e A085580 10 .. 11 ..... 3 ..... 0.92261628933
%e A085580 11 .. 12 ..... 5 ..... 0.928203230275
%e A085580 12 .. 13 ..... 2 ..... 0.9330343736592
%e A085580 13 .. 14 ..... 7 ..... 0.93725393319377
%e A085580 14 .. 15 ..... 6 ..... 0.940971508067066
%e A085580 15 .. 16 ..... 7 ..... 0.9442719099991587
%e A085580 Note that if n=0 then d = golden ratio phi, minus 1 = 0.61803398874989484820...
%o A085580 (PARI) superdiagonal(n,n1) = { default(realprecision,n); b= ""; j=1; 
               for(k=1,n1, v = ""; for(m=1,n, s=.1; for(x=1,n, s=k/(s+m); ); a = 
               Vec(Str(s)); v = concat(v,a[m+2]); ); a2 = Vec(Str(v)); print1(a2[k]",
               "); ) }
%Y A085580 Sequence in context: A021617 A140321 A019979 this_sequence A092151 A066717 
               A154969
%Y A085580 Adjacent sequences: A085577 A085578 A085579 this_sequence A085581 A085582 
               A085583
%K A085580 easy,nonn
%O A085580 0,1
%A A085580 Cino Hilliard (hillcino368(AT)gmail.com), Jul 06 2003
%E A085580 Edited (with examples) by Omar E. Pol (info(AT)polprimos.com), Mar 27 
               2008