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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). 9
3, 32, 37, 64, 533, 960 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A119937 A254312 A304048 * A197368 A114257 A197524
KEYWORD
nonn,base,fini,full
AUTHOR
Paolo P. Lava, Feb 18 2019
EXTENSIONS
a(6) added by Giovanni Resta, Feb 20 2019
STATUS
approved

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Last modified February 26 02:39 EST 2024. Contains 370335 sequences. (Running on oeis4.)