A124798 Sequence of digits (least significant digit first) of A124797 (sums of cyclic permutations of 1...n written in base n+1).

1, 0, 1, 1, 2, 3, 3, 1, 0, 2, 2, 2, 2, 3, 5, 5, 5, 5, 2, 0, 3, 3, 3, 3, 3, 3, 4, 7, 7, 7, 7, 7, 7, 3, 0, 4, 4, 4, 4, 4, 4, 4, 4, 5, 9, 9, 9, 9, 9, 9, 9, 9, 4, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 5, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 13, 13, 13, 13, 13, 13

Offset: 1

Author

M. F. Hasler, Nov 07 2006

Keywords

• base
• easy
• nonn

Comments

Sequence A083956 becomes "unnatural" for n>9. It is easily seen that for n=2k, the sum of permutations A124797(n) is {k:n}0 in base n+1 where {k:n} means n times the digit k; while for n=2k+1 (>1), the sum is k{n:2k}{k+1} (again in base n+1). In particular, this number has n+1 digits (for n>1), such that the digits for A124797(n) start at place n(n+1)/2-1 (for n>1).

Examples

			a(1)=1, the sum of cyclic permutations of 1;
a(2..4)=0,1,1 since 12 + 21 = 110 in base 3;
a(5..8)=2,3,3,1 since 123 + 231 + 312 = 1332 in base 4;
a(9..13)=0,2,2,2,2 since 1234 + 2341 + 3412 + 4123 = 22220 in base 5.
		

Crossrefs

Cf. A083956, A124797.

Programs

Maple

A124797 := n->(n+1)/2*((n+1)^n-1): map(op, [ 'convert(A124797(i),base,i+1)' $ i=1..20 ]);