A340208 Constant whose decimal expansion is the concatenation of the smallest n-digit cube A061434(n), for n = 1, 2, 3, ...
1, 2, 7, 1, 2, 5, 1, 0, 0, 0, 1, 0, 6, 4, 8, 1, 0, 3, 8, 2, 3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 7, 7, 6, 9, 6, 1, 0, 0, 5, 4, 4, 6, 2, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 7, 8, 7, 3, 8, 7, 5, 1, 0, 0, 0, 2, 6, 5, 7, 7, 2, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
Offset: 0
Examples
The smallest cube with 1, 2, 3, 4, ... digits is, respectively, 1, 27 = 3^3, 125 = 5^3, 1000 = 10^3, .... Here we list the sequence of digits of these numbers: 1; 2, 7; 1, 2, 5; 1, 0, 0, 0; ... This can be considered, as for the Champernowne and Copeland-Erdős constants, as the decimal expansion of a real constant 0.1271251000106481... As a triangle, in which row n contains the decimal expansion of the smallest n-digit cube: 1 2 7 1 2 5 1 0 0 0 1 0 6 4 8 1 0 3 8 2 3 1 0 0 0 0 0 0 1 0 0 7 7 6 9 6 ...
Links
- Zhuorui He, Table of n, a(n) for n = 0..11324 (first 150 rows)
Crossrefs
Programs
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PARI
concat([digits(ceil(10^((k-1)/3))^3)|k<-[1..14]]) \\ as seq. of digits c(N=12)=sum(k=1,N,.1^(k*(k+1)/2)*ceil(10^((k-1)/2))^2) \\ as constant
Formula
c = 0.12712510001064810382310000001007769610054462510000000001000787387510002657...
= Sum_{k >= 1} 10^(-k(k+1)/2)*ceiling(10^((k-1)/3))^2
a(-n(n+1)/2) = 1 for all n >= 2;
a(k) = 0 for -3n(3n+1)/2 > k > -(3n+1)(3n+2)/2, n >= 0.
Comments