A083956 a(n) = sum of all cyclic permutation of concatenation of first n numbers. In each case the digits of a number are kept together for n>9.

1, 33, 666, 11110, 166665, 2333331, 31111108, 399999996, 4999999995, 509876543215, 52098641976336, 5331076296399558, 546238942849832881, 56038035699304276305, 5755318721445859729830, 591693488306202516193456

Offset

1,2

Comments

Initial terms are {n(n+1)/2}*{A000042(n)}.

Links

Table of n, a(n) for n=1..16.

Example

a(1) = 1, a(2) = 12 + 21, a(3) = 123 + 231 + 312 = 666.
a(11) = 1234567891011 + 2345678910111 + ... + 1011123456789 + 1112345678910.

Maple

# count digits in positive integer digs := proc(inp::integer) local resul, shiftinp : resul := 1 : shiftinp := iquo(inp, 10) : while shiftinp > 0 do resul := resul+1 : shiftinp := iquo(shiftinp, 10) : od : RETURN(resul) : end: # provide number of concatenation up to lst, permuted by cycl newnum := proc(lst::integer, cycl::integer) local resul, i, insrt : resul := 0 : for i from 1 to lst do insrt := ((i+cycl-1) mod lst) +1 : resul := resul*10^digs(insrt)+insrt : od : RETURN(resul) ; end : n := 2 : while n < 13 do su := 0 : for cycl from 0 to n-1 do # print(n, " add ", newnum(n, cycl)) ; su := su + newnum(n, cycl) : od : printf("%a, ", su) : n := n+1 : od : # R. J. Mathar, Mar 13 2006
A083956 := n -> add( convert( cat( 'modp(j+i, n)+1' $ j=1..n ), decimal, 10), i=1..n ); # M. F. Hasler, Nov 08 2006

Crossrefs

Cf. A083957.

Sequence in context: A261486 A094760 A365645 * A164761 A028210 A028205

Adjacent sequences: A083953 A083954 A083955 * A083957 A083958 A083959

Keyword

base,nonn

Author

Amarnath Murthy, May 10 2003

Extensions

More terms from R. J. Mathar, Mar 13 2006

Further terms from M. F. Hasler, Nov 08 2006

Status

approved