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
Examples
a(1) = 1, a(2) = 12 + 21, a(3) = 123 + 231 + 312 = 666. a(11) = 1234567891011 + 2345678910111 + ... + 1011123456789 + 1112345678910.
Crossrefs
Cf. A083957.
Programs
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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
Extensions
More terms from R. J. Mathar, Mar 13 2006
Further terms from M. F. Hasler, Nov 08 2006
Comments