A324223 - OEIS

A324223

a(n) is defined by the condition that the decimal expansion of Sum_{n>0} 1/a(n)^n = 1/a(1)^1 - 1/a(2)^2 + 1/a(3)^3 - ... begins with the concatenation of these numbers; also a(1) = 3 and a(n) > a(n-1).

3, 32, 37, 64, 533, 960

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OFFSET

1,1

COMMENTS

a(6) is the last term because the sequence cannot be extended. At any step a(n) is chosen as the least number greater than a(n-1) that meets the requirement. Up to 960 the sum is 0.3 32 37 64 533 960 0692... and the zero after 960 cannot be removed.

If the limitation a(n) > a(n-1) were removed then the sequence would be 3, 32, 37, 22, 48 and 48 would be the last term because after it the sum presents 0911... and the zero cannot be removed. - Giovanni Resta, Feb 20 2019

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

1/3^1 = 0.3333...

1/3^1 - 1/32^2 = 0.332356...

1/3^1 - 1/32^2 + 1/37^3 = 0.33237651...

The sum is 0.3 32 37 64 533 ...

MAPLE

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

d:=h; print(d); t:=2; for n from 1 to q do

if trunc(evalf(a+(-1)^(t+1)/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+(-1)^(t-1)/n^t; t:=t+1;