A193381 Largest multiple of n which is a concatenation of the n numbers n(n-1)/2,...,n(n+1)/2-1, or 0 if no such number exists.

0, 12, 543, 9876, 1413121110, 201918171516, 27262524212322, 3534333231302928, 444342414039383736, 54535251494847464550, 6564636261605958575655, 777675747372717069676668, 90898887868584838281798078, 999897969594939291104103101102100

Offset: 1

Author

M. F. Hasler, Jul 24 2011

Keywords

• nonn
• base

Comments

This is to A192392 what is A080481 to A053067: The integers are considered in groups of n=1,2,3,... numbers, starting with {0}, {1,2}, {3,4,5}, ... The sequence lists the concatenation of the permutation of the n elements of each group which yields the largest multiple of n, when written in decimal.

Examples

			a(20) = concat(210,209,...,201,199,...,191,200).
		

Programs

Mathematica

lmn[n_]:=Max[Select[FromDigits[Flatten[IntegerDigits/@#]]&/@Permutations[n],Divisible[ #,Length[n]]&]]; Join[{0},lmn/@With[{nn=10},TakeList[Range[(nn(nn+1))/2],Range[2,nn]]]] (* The program generates the first 10 terms of the sequence. To generate more, increase the nn constant but the program may take a long time to run. *) (* Harvey P. Dale, Nov 20 2023 *)

PARI

a(n)={my(d=vecsort(vector(n,i,Str(n*(n-1)/2-1+i)),,4),t); for(i=1,n!, eval(concat(d))%n || return(eval(concat(d))); d=precperm(d))} /* see A076072 for precperm() */