A337692 a(n) is the sum of all positive integers whose digits in base n are strictly decreasing.
0, 3, 40, 495, 6816, 108255, 1980672, 41289759, 968750080, 25296994503, 728148203520, 22912992806847, 782690956959744, 28847447610890415, 1141156999457800192, 48228647947883167935, 2168834125678237974528
Offset: 1
Examples
In base n=3, a(3) is the sum of the base-3 numbers {1, 2, 10, 20, 21, 210}, which sum to 1+2+3+6+7+21 = 40.
Links
- Reddit user blungbat, Sum of numbers with descending digits II, r/mathriddles, 2020.
Programs
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Maple
rebase := proc(digs,b) add( op(i,digs)*b^(i-1),i=1..nops(digs)) ; end proc: A337692 := proc(b) local a,digs,len,p ; a := 0 ; digs := [seq(i,i=0..b-1)] ; for len from 1 to b do for p in permute(digs,len) do if op(-1,p) <> 0 and sort(p) = p then print(p) ; a := a+rebase(p,b) ; end if; end do: end do: print() ; a ; end proc: seq(A337692(n),n=1..8) ; # R. J. Mathar, Nov 20 2020