A324222 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, 6, 14, 75, 574, 2029, 4589, 7927, 78325, 681667, 720945

Offset

1,1

Comments

a(11) 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 720945 the sum is 0.3 6 14 75 574 2029 4589 7927 78325 681667 720945 0664... and the zero after 720945 cannot be removed.

If the limitation a(n) > a(n-1) were removed then the sequence would be 3, 6, 14, 75, 57, 58, 91, 197, 53, 423, 613, 102, 956 and 956 would be the last term because after it the sum presents 0316... and the zero cannot be removed. - Giovanni Resta, Feb 20 2019

Links

Table of n, a(n) for n=1..11.

Example

1/3^1 = 0.3333...
1/3^1 + 1/6^2 = 0.36111...
1/3^1 + 1/6^2 + 1/14^3 = 0.3614755...
The sum is 0.3 6 14 75 574 ...

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/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/n^t; t:=t+1;
print(n); fi; od; end: P(10^5, 3);

Crossrefs

Cf. A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305667, A305668, A320023, A320284, A320306, A320307, A320308, A320309, A320335, A320336, A324223.

Sequence in context: A257320 A318344 A129090 * A058141 A144654 A132279

Adjacent sequences: A324219 A324220 A324221 * A324223 A324224 A324225

Keyword

nonn,base,fini,full

Author

Paolo P. Lava, Feb 18 2019

Extensions

a(7)-a(11) added by Giovanni Resta, Feb 20 2019

Status

approved