A171725 6-digit numbers k such that: (a) the digits of k are from the set {1, 2, 3, 4, 5}, and (b) any digit that appears in k appears at least twice.

111111, 111122, 111133, 111144, 111155, 111212, 111221, 111222, 111313, 111331, 111333, 111414, 111441, 111444, 111515, 111551, 111555, 112112, 112121, 112122, 112211, 112212, 112221, 112222, 112233, 112244, 112255, 112323, 112332, 112424, 112442, 112525, 112552

Offset

1,1

Comments

See Problem 4 of RMO 2007 (Regional Mathematical Olympiad-India).

There are exactly 1405 such numbers from 111111, 111122,... to ..., 555544, 555555.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..1405 (full sequence)

|nSan|ty, RMO 2007 problem

Maple

A171725:={}: for n from 9331 to 46655 do d:=convert(n, base, 6): for k from 0 to 5 do cordig:=true: if((k=0 and numboccur(k, d)>0) or (k>0 and numboccur(k, d)=1))then cordig:=false:break: fi: od: if(cordig)then A171725 := A171725 union {op(convert(d, base, 10, 10^nops(d)))}: fi: od: op(sort(convert(A171725, list))); # Nathaniel Johnston, Jun 24 2011

Mathematica

cc=0; re=Reap[Do[dc=DigitCount[n]; If[Take[dc, {6, 10}]=={0, 0, 0, 0, 0}&&FreeQ[Take[dc, 5], 1], cc++; Sow[n]], {n, 111111, 555555}]][[2, 1]]; cc

Crossrefs

Sequence in context: A205243 A223110 A094325 * A135403 A154549 A038448

Adjacent sequences: A171722 A171723 A171724 * A171726 A171727 A171728

Keyword

base,fini,full,nonn

Author

Zak Seidov, Dec 16 2009

Status

approved