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

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;
print(n); fi; od; end: P(10^6, 3);

Crossrefs

Cf. A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305667, A305668, A320023, A320284, A320306, A320307, A320308, A320309, A320335, A320336, A324222.

Sequence in context: A119937 A254312 A304048 * A197368 A114257 A197524

Adjacent sequences: A324220 A324221 A324222 * A324224 A324225 A324226

Keyword

nonn,base,fini,full

Author

Paolo P. Lava, Feb 18 2019

Extensions

a(6) added by Giovanni Resta, Feb 20 2019

Status

approved