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%I #14 Jan 12 2021 09:06:37
%S 0,3,40,495,6816,108255,1980672,41289759,968750080,25296994503,
%T 728148203520,22912992806847,782690956959744,28847447610890415,
%U 1141156999457800192,48228647947883167935,2168834125678237974528
%N a(n) is the sum of all positive integers whose digits in base n are strictly decreasing.
%H Reddit user blungbat, <a href="https://www.reddit.com/r/mathriddles/comments/it24bd/sum_of_numbers_with_descending_digits_ii/">Sum of numbers with descending digits II</a>, r/mathriddles, 2020.
%e 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.
%p rebase := proc(digs,b)
%p add( op(i,digs)*b^(i-1),i=1..nops(digs)) ;
%p end proc:
%p A337692 := proc(b)
%p local a,digs,len,p ;
%p a := 0 ;
%p digs := [seq(i,i=0..b-1)] ;
%p for len from 1 to b do
%p for p in permute(digs,len) do
%p if op(-1,p) <> 0 and sort(p) = p then
%p print(p) ;
%p a := a+rebase(p,b) ;
%p end if;
%p end do:
%p end do:
%p print() ;
%p a ;
%p end proc:
%p seq(A337692(n),n=1..8) ; # _R. J. Mathar_, Nov 20 2020
%K nonn,base
%O 1,2
%A _Jason Lang_, Sep 15 2020
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