A077688 - OEIS

%I #10 Jun 08 2019 17:57:49

%S 1,55,1665,269884,6565656565,1121212121211,176767676767675,

%T 26262626262626260,3727272727272727269,510101010101010101005,

%U 67777777777777777777771,8787878787878787878787870,1116161616161616161616161605

%N a(n) = sum of all cyclic permuted concatenations of the next n numbers.

%F For n not in A068092 (implying that all n numbers in the concatenation have the same length L), a(n) = ((n^2+1)*n)/2 * (10^(L*n)-1)/(10^L-1), where L = ceiling(log(n^2/2)/log(10)). - _Max Alekseyev_, Feb 11 2005

%e a(2) = 23 + 32, a(4) = 78910 + 89107 + 91078 + 10789 = 269884 = sum of concatenation of numbers in each group: (7,8,9,10), (8,9,10,7), (9,10,7,8), (10,7,8,9).

%o (PARI) { len10(n) = ceil(log(n+1)/log(10)) } { A077688(n) = local(m,w,s); m=0; for(k=1+(n*(n-1))/2,(n*(n+1))/2, m=m*10^len10(k)+k ); w=10^len10(m); s=0; for(k=1+(n*(n-1))/2,(n*(n+1))/2, m=(m*10^len10(k)+k)%w; s+=m ); return(s); } \ for n not in A068092 { a(n) = local(l); l=len10(n^2/2); return((n^2+1)*n*(10^(l*n)-1)/(10^l-1)/2) } \\ _Max Alekseyev_, Feb 11 2005

%Y Cf. A068092, A000217.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Nov 16 2002

%E More terms from _Max Alekseyev_, Feb 11 2005