A260858 Base-8 representation of a(n) is the concatenation of the base-8 representations of 1, 2, ..., n, n-1, ..., 1.
0, 1, 81, 5329, 342225, 21911761, 1402427601, 89755965649, 45954960939217, 188231512819194065, 770996276517410920657, 3158000748616424634669265, 12935171066332946781853145297, 52982460687699754593548358342865, 217016158976818195107979529799293137
Offset: 0
Examples
a(0) = 0 is the result of the empty sum corresponding to 0 digits. a(2) = 81 = (8+1)^2 = 8^2 + 2*8 + 1 = 121_8, the concatenation of (1, 2, 1). a(9) = 12345671011107654321_8, concatenation of (1, 2, 3, 4, 5, 6, 7, 10, 11, 10, 7, 6, 5, 4, 3, 2, 1), where the middle "10, 11, 10" are the base-8 representations of 8, 9, 8.
Links
- D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015
Programs
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PARI
a(n,b=8)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))
Formula
For n < b = 8, we have a(n) = A_b(n) = R(b,n)^2, where R(b,n) = (b^n-1)/(b-1) are the base-b repunits.
Comments