A320307 - OEIS

A320307

Numerators of the fractions a(0)/(a(1) - a(0)), a(1)/(a(2) - a(1)), a(2)/(a(3) - a(2)), ... such that the sum 1/a(0) + Sum_{n>=1} a(n-1)/(a(n) - a(n-1)) has the concatenation of these numerators as decimal part. Case a(0) = 10.

10, 3167, 9115670120, 542008360464753577575056956, 7830689983639267579884170593492086524040157478312672952864203282974067

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OFFSET

0,1

COMMENTS

It appears that fractions of this kind exist only for a(0) equal to 3 (A320306), 10 (this sequence), 13 (A320308) and 38 (A320309).

Next term has 184 digits. - Giovanni Resta, Oct 11 2018

LINKS

Table of n, a(n) for n=0..4.

EXAMPLE

1/10 = 0.1000...

1/10 + 10/(3167 - 10) = 0.103167564...

1/10 + 10/(3167 - 10) + 3167/(9115670120 - 3167) = 0.1031679115670120373...

The sum is 0.10 3167 9115670120 542008360464753577575056956 ...

MAPLE

P:=proc(q, h) local a, b, d, n, t, x; x:=h+1; a:=1/h; b:=ilog10(h)+1;

d:=h; print(d); t:=1/a; for n from x to q do if

trunc(evalf(a+t/(n-t), 100)*10^(b+ilog10(n)+1))=d*10^(ilog10(n)+1)+n

then b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; a:=a+t/(n-t); t:=n;

x:=n+1; print(n); fi; od; end: P(10^20, 10);

CROSSREFS

Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A320306, A320308, A320309.

Sequence in context: A123377 A061543 A305666 * A225764 A243008 A133198

Adjacent sequences: A320304 A320305 A320306 * A320308 A320309 A320310

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Oct 11 2018

EXTENSIONS

a(3)-a(5) from Giovanni Resta, Oct 11 2018

STATUS

approved