A085580 a(n) = (n+1)-st digit after decimal point of d, where d = (sqrt((n+1)^2 + 4(n+1)) - (n+1))/2.

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..99.

Example

===============================================================
n ... n+1 ... a(n) ... Value of d with first n+1 decimals only
===============================================================
0 ... 1 ...... 6 ..... 0.6
1 ... 2 ...... 3 ..... 0.73
2 ... 3 ...... 1 ..... 0.791
3 ... 4 ...... 4 ..... 0.8284
4 ... 5 ...... 0 ..... 0.85410
5 ... 6 ...... 3 ..... 0.872983
6 ... 7 ...... 1 ..... 0.8874821
7 ... 8 ...... 8 ..... 0.89897948
8 ... 9 ...... 3 ..... 0.908326913
9 ... 10 ..... 0 ..... 0.9160797830
10 .. 11 ..... 3 ..... 0.92261628933
11 .. 12 ..... 5 ..... 0.928203230275
12 .. 13 ..... 2 ..... 0.9330343736592
13 .. 14 ..... 7 ..... 0.93725393319377
14 .. 15 ..... 6 ..... 0.940971508067066
15 .. 16 ..... 7 ..... 0.9442719099991587
Note that if n=0 then d = golden ratio phi, minus 1 = 0.61803398874989484820...

Prog

(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]", "); ) }

Crossrefs

Sequence in context: A021617 A140321 A019979 * A092151 A365477 A066717

Adjacent sequences: A085577 A085578 A085579 * A085581 A085582 A085583

Keyword

easy,nonn,base

Author

Cino Hilliard, Jul 06 2003

Extensions

Edited (with examples) by Omar E. Pol, Mar 27 2008

Status

approved